I use the caulk gun and the I wet my finger and wipe it smooth. Works for me.
If it’s acrylic caulking, yep. All you need is a slightly wet rag, folded perfectly, giving you numerous finger wipes before having to rinse it all out. Lord I can’t even begin to think of how many tubs, showers, around sinks, C-tops, toilets, even all around the bottom of baseboards I’ve done while I was a make-ready guy in the apartment world.
Silicone caulking? You’re on your own. I hate using it inside for anything(even though I kinda love the smell)