Yes, your "instincts" are good.
Either way- either remove the contamination first, then dampen a paper towel* w/ F10 (or other product such as diluted chlorhexidine) to wipe the dirty area of the "floor" of the tub/enclosure/tank without dampening the surrounding substrate (*I don't spray the F10 or other products with the snake present), or just use a water-dampened paper towel to wipe up the dirty area, & wait to use the F10 (etc) when doing a full substrate change- your choice.
Much of a snake's "output" ends up powdery, so it's hard to track it all down once it's dry & in the substrate- so I grab the substrate that surrounds what I've picked up, then wipe- sounds like that's what you're doing too. I'm with you- I don't spray with a snake present, but it's fine to dampen the paper towel you wipe up with- wipe it dry & throw substrate back over it.