During this year we noticed water marks on our kitchen ceiling and at one point the paint tore due to water forming up top. At the time it was attributed to a leaky toilet (the insides were old so the tank kept overflowing which eventually damaged our kitchen ceiling below). I fixed it, and for a time it was okay. Now the water damage came back, and now we see it's because the shower (we have no tub in our house, they took it out to install the shower for more closet space there) only has a wooden frame along the outside and was never caulked. Cue dramatic drum music here.

So today is my day to caulk it, and that's where the misadventures begin. From all accounts it seemed easy enough (though it took a few minutes and a few curse words to figure out the caulking gun) but unfortunately when I used the spout cutter it cut the hole way too big so I ended up using too much caulk.

My question is, should I try to clean it all up quickly and re-caulk, or let it dry then just clean up the excess? I'm going more with the latter than the former.