The problem there, I think, is that the Punjab is simply too critical to the Raj's food supply for them to ignore. Nepal was relatively small and out-of-the-way - but the Punjab is huge population-wise and tremendously important, even before the Green Revolution. If the British don't have direct control, they'll want it to be firmly under their thumb. And then the Sikh state becomes just another ineffective princely state to be subsumed into India or Pakistan or whatever comes after the Raj.
Cheers,
Ganesha
Not really. Of course, the Sikh Empire is clearly too valuable a prize to be left alone to its own devices by the British East India Company, but they don't have to be left alone to retain independence. All they have to do is to hold out against the British until the Great Indian Mutiny takes place. Having a feasible POD that would have led to Sikh victory over the British at the Battle of Ferozeshah in the 1st Anglo-Sikh War- a split second decision, the slightest alteration to the trajectory of a bullet or a cannonball, one of the incompetent/treacherous Dogra commanders being killed or injured in the course of battle and being relieved of command by a more capable/loyal Sikh commander- would be the easiest thing in the world to conceive happening.
Such a victory would be a huge setback for the British campaign, and would at the very least lead to easier terms in the treaty which brings the war to an end, with the territory of the Jalandhar Doab almost certainly staying in their hands. After this, in all likelihood, the British treat the Anglo-Sikh War in the same manner as the Anglo-Afghan War (OTL's 1st, but probably the only one ITTL)- as a rash, unnecessary and ill-prepared campaign, with no need to repeat the debacle by rushing into a second attempt at conquest. The BEIC would build up a massive army in NW British India over time, ready and waiting to wage war with the Sikh Empire and bring them under their control in one fell swoop when the opportunity presents itself- a strategy which hits the fan for them in 1857, creating a much larger combat force of far better-equipped Indian insurgents than IOTL's Sepoy Mutiny, and giving them a far greater chance of success in the ensuing conflict- a fact which won't go unnoticed by several princely states' leaders, with at least a few ditching their neutrality and joining the rebels' cause ITTL, further boosting their chances of overthrowing company rule.
If the rebels achieve their goal of independence though, at least across a contiguous region of North, West and Central India, then it still wouldn't be the 'Indian First War of Independence' that Indians refer to it as in their textbooks and classrooms IOTL. If you're looking for a more Balkanised India in your timeline, then there's surely no other way you could go about it that would lead to a more certain outcome. You'd have the Mughals, the Marathas and Awadh, plus any other former princely states that managed to cast off the yoke of British oppression. Would the reinstated Mughals be willing to grant the other parties in their successful revolution enough freedom and independence to keep them united? Could they have done so? Or would the other major parties involved, the Maratha states and the Nawab of Awadh in particular, have refused to integrate into the new 'Mughal Confederacy', determined to never again let their kingdoms fall under the control of another domineering empire? Conversely, even if the rebels fail and things eventually play out exactly as they did IOTL, with the end of company rule and the establishment of the British Raj, the newly instated Viceroy would be extremely unlikely to make another attempt to conquer the Sikh Empire outright, especially in light of the Khalsa's reaction and conduct during the Great Indian Mutiny...
Based on OTL's Punjab during the crisis IOTL, this would have likely been either one of cold indifference, keeping out of the hostilities and allowing both sides to kill as many of each other as they liked; or, perhaps more likely, one of horrified consternation at the possible resurgence of the Mughal Empire. After all, which Empire carried out the executions of three of the Sikhs' Gurus, along with countless other martyrs, all in the most brutal and barbaric manner possible? Being burnt to death on a hot plate, beheaded, boiled in a pan, sawn in half from the bottom up, bricked alive (this method being used to execute Guru Gobind Singh's two youngest sons, who were only 9 and 7 years old respectively), only 150 years or so prior to the Mutiny (as recent in their timeframe as Lincoln's Emancipation Proclamation is in ours)... The first attempt to establish a Sikh state was crushed by the Mughals in 1715, the first iteration of the Dal Khalsa under Banda Singh Bahadur killed off to the last man in an attack waged by the entire Imperial force- with the sole exception of Banda Singh and 700 prisoners of war, including his son, who were all taken back to Delhi to face public execution on a daily basis. Banda Singh's son was castrated before being killed, with the body parts force-fed down Banda's throat; and when it was his turn, several months later, Banda Singh first had his eyes gouged out, limbs chopped off and skin peeled off before finally being executed.
Afterwards, the Mughals deployed a standing army dedicated solely to carrying out a genocidal campaign against them, with the Sikh people and the Sikh faith only managing to endure by retreating to the hills and waging a guerrilla campaign for a full 25 years. For them, at the time of the Indian mutiny, it'd be a trauma just as recent as, and quite possibly, even more harsh a memory than, the rule of the Congo Free State would be to the people of the DRC today- or even that of Nazi Germany will be for the Jewish people by the time we reach the halfway point in this century. The British were merely relatively recent foes in a single, pretty short and honourably fought war, one which resulted in a Sikh victory/considerably more acceptable terms at the negotiating table than IOTL's 1st Anglo-Sikh War. In comparison, the prospect of the Mughal Empire rising again would perhaps be as nightmarish for the Sikh Empire as that of a Neo-Nazi, anti-Semitic unified Arab state might have been for the Israelis in an ATL's more visceral version of the Arab Spring. It'd be all too feasible to imagine the Sikhs offering to send the Khalsa army across the border to fight alongside the British, determined to crush those determined to restore the power of the Mughal Empire and calling for Jihad.
There’s no way the British, certainly not the BEIC, would turn down the Sikhs’ offer in the position they’d be in; and the Sikhs’ assistance in quelling the Great Indian Mutiny would be invaluable, vastly greater both in its military strength and strategic importance than that of Nepal’s Gurkhas ITTL. In the aftermath of the conflict, with the brownie points the Sikhs would earn for their contribution from both the British Raj in India and the British public back home, even the least grateful, most imperialistic Viceroy of India would have had a hard time drumming up support to wage war on the Sikhs again and annex their Kingdom. From this point, you could easily imagine the British granting the Sikhs some reward for their part from the war effort (perhaps territory in Himachal Pradesh, the British Punjab or the Upper Sindh, seized from rebellious Rajas or Nawabs), building friendly diplomatic relations with them, and eventually extending them some formal friendship agreement in the same manner as they did with Nepal IOTL.
Or, indeed, as they did with OTL's Empire of Japan by signing the Anglo-Japanese Alliance with them- probably a better model, given that both the Japanese Empire and Sikh Empire are estimated to have possessed roughly the same wealth and population at the time of the Indian Mutiny, a decade prior to the Meiji Restoration. The Anglo-Japanese Alliance certainly helped the Japanese in modernising their infrastructure, economy and especially their military IOTL, essentially granting them free range to embark on their campaign of Imperial expansion and to become the only non-western World Power. Why couldn't TTL's Anglo-Sikh Alliance be the key contributing factor which allows the Sikh Empire to modernise, and to earn its status as a World Power, in the same way as the Empire of Japan? Backed by the British, who have no choice but to either concede defeat to Russians in The Great Game or continue it by proxy, the battlefields of Central Asia and its Khanates await...