Oh, and if you don’t intend to dismantle the watch and have the case ultrasonically cleaned, a trick I use for “dry cleaning” on non-water proof cases is to use naphtha (lighter fluid) on a paper towel and my fingernail running around the bezels, case back, etc to get the gunk off. It evaporates almost immediately, leaves no residue and is safe on acrylic- all the art conservators I know keep a gallon jug on hand all the time.
You can also use a toothbrush with the naphtha to loosen all the funk and wipe off with a naphtha damp paper towel.