You can also finish the inside parts of the box prior to assembly. It doesn't have to be perfect, since you can apply another coat after you cut the lid off, but that way you should be able to remove the glue fairly easily.
The challenge then shifts from not getting finished onto the tail and pins because that impacts the glue strength. As long as you're reasonably careful that shouldn't be an issue, dovetails are strong by themselves, and it's not like a box sees a lot of mechanical stress.
A long time ago I bought something called Waxalit. It's a wax used for lubricating tools surfaces, e.g. table saw top. It also works as a glue release agent. I'd dry assemble the piece, brush on the wax along the edges where the glue would squeeze out, let the wax dry, then do a glue up as normal. Dried up glue pops off like magic, then just a little cleanup with mineral spirits. They don't sell it Waxilit anymore, but I imagine that any mold release wax would also work.
But yeah, tape works too.