No one has ever been anywhere near good enough at Pauline hat jumps to reach the top of that skyscraper, so no one really has an exact method. I'd suggest just starting at the south end of the mainland and aiming north though. If you actually manage to make it up there, I'll eat a hat (Pauline's hat perhaps)

The thing here is that 2P is much less frequently run that 1P any%, so it's unlikely that anyone will put in the effort to learn this strat regardless. My theorized route would actually be to clip into the ground and grab the chest moon as Mario while Cappy activates the checkpoint on the island, which might be the only way to do the skip with it being faster than the standard route (and this seems like a TAS only idea to me). Most likely, it isn't even faster at all. Just spitballing here, I don't know a whole lot about how the skip works since I haven't personally tried it.

It's currently only possible in 2-player mode. It's possible that this could save time in a 2P any% TAS, but I suspect it's far too difficult to save time in runs done by humans.