Probably don't need the soap either, just water is all I can remember using to clean up a snake after egg-laying.
I personally have never (& would never) use F10 or chlorhexidine ON the snake itself, perhaps because I read & take the label precautions seriously, & because like us,
snakes can absorb things thru their skin; like ours, their bodies depend on "friendly bacteria" to function, and such products do not discriminate, so I remain cautious.
To me, F10 & chlorhexidine are great to clean cages & implements, but not for use on the snakes themselves. Can you do it & have some gotten away with
doing this? -those are different questions & one we each have to answer for ourselves, I guess.