I've done both - let the squeeze-out "semi-set" and then use a chisel (which I keep for this very purpose) to lift it off. I used to use a damp rag, but find that the chisel works best for me.
Whichever method you use, they both work.
Just a thought - before applying your finish, wipe on a solvent of some kind (methyl hydrate, paint thinner, whatever you have handy that is clear) - this will show MANY imperfections in your work - including glue smudges. I use some chalk to mark the trouble areas, and when the solvent evaporates fix the problem before finishing.