Well there are a couple of problems I foresee, not insurmountable ones, mind you but problems. The first being that the Knights of St. John at the time of the 18th century still regarded themselves as an exclusively anti-Muslim organization. One of the main arguments for NOT resisting Napoleon was that his troops were culturally Christian. The other problem I see is that there were substantial numbers of Frenchmen in the Knights of St. John, all of whom were less than enthusiastic about fighting their countrymen.
As for overcoming these problems, I guess you could have the Knights brand Napoleons' troops as Jacobins (however inaccurate that may be, it just might work in circumventing the whole "Christian" thing) and perhaps the French Knights are influenced by disaffected refugees from the Vendee joining the Order earlier on.
Assuming that the hurdles which led to them capitulating in OTL are dealt with, the battle itself could go either way in my opinion. First of all it should be noted that the French arrival was greeted with a revolt of the local population, who were eager to see the primarily foreign born knights, kicked off the island. This means that unlike the 16th century battle of Malta, TTL's Knights will not have the support of the locals. This means that holding the city is going to be impossible and the Knights are going to have to retreat to their fortress(es) on the island. Whether or not these fortresses are adequately prepared will define the battle. If they're not then it goes much like OTL, perhaps a few days longer.
Given that the Knight's fortifications are built in such a way that they dominate the harbor and are capable of raining fiery death on the French ships, Napoleon is forced to either deal with the forts or try to resupply under fire (however limited that may be...) and continue on to Egypt.
Worst Case Scenario for Napoleon: The Knights are prepared for his arrival and send word to the British. Napoleon invades Malta and with the help of the local Maltese drives the Knights of St. John back to their fortification which has been filled to the gills with all possible supplies to resist the French. Here Napoleon is forced into a siege like situation and delayed long enough to allow the Royal Navy to arrive and inflict a decisive defeat on the French fleet/army. Napoleon is captured/killed and history is forever changed.