I'm a bit surprised I haven't seen anyone post the obvious way--or what seemed the obvious way to me, anyway--to do this, which is to avoid World War I and World War II altogether. Without battle experience pointing the way away from battleships, they'll likely remain one of the major elements of any fleet that can afford them for quite a while longer than OTL, more than long enough to overlap with the development of nuclear power (remember, navies were early on the nuclear trend...). Once you have that it's no great shake to have one or a few powers commission at least some trial battleships to see if nuclear battleships offer any substantial advantages over conventional ones.
I'm not sure why you think "the ability to be sent anywhere in the world" is a trivial or meaningless capability; in fact lining up all the logistical ducks to allow going anywhere in the world consumed quite a substantial amount of time in all the major admiralties from the inception of the battleship onwards. You just have to look at the efforts taken by the Russians to reach Tsushima or the development of underway refueling by the United States to see how much energy it took to actually get the battle fleet forwards. Nuclear power pretty much cuts that all out, at least for the ships that have it.
The problem is that even without WWI and WWII the battleship is likely going to be on the way out by the late 1940s.
The first thing, and without the World Wars the most important one, is that by the end of WWII battleship design had run headlong into diminishing returns as applied to the cost/firepower curve. While this starts becoming noticeable with the post-treaty generation - the Littorio and Bismarck classes, despite displacing north of 40,000 tons, had firepower not much greater than what 30,000-ton ships had carried twenty years prior, and the Yamatos were over 15,000 tons heavier than, say, an N3 - it's really noticeable with the 1944 design studies for the Lions. Despite staying at 9 16" guns and reducing speed to 26 knots, the design ballooned to nearly 60,000 tons entirely through the demands of enhanced horizontal and underwater protection, and it defied all attempts to go below 55,000 tons without reducing the main battery. It was so bad that the DNC concluded that "the power of modern weapons had increased so much that ever-increasing armour and torpedo protection was required until it became incompatible with the limited offensive power of the ship."
And this isn't something that's likely to go away without the World Wars. Navies were always interested in finding new ways to sink battleships without having to invest in battleships themselves. Investing in more powerful torpedoes is
definitely something navies would be all over, as would anything that lets horizontal bombing actually
hit something as well once bombers enter the picture.
Then again, if the naval arms race isn't arrested at some point in the 1920s it's liable to escalate to the point of crippling size and cost. The US Navy was already preparing to escalate above 50,000 tons. Either way, at some point there's going to be a sanity check.
The second thing is that while no World Wars is going to slow the transition from battleships to carriers as the battle force, it's not going to stop it. The US Navy was heading in that direction already in 1940, with the Two-Ocean Navy Act being biased far more towards carriers than battleships.
