If you treat with the Provent a Mite, this isn't needed. It sounds like you have things well in hand. You can soak the snake before hand with a drop or two of soap. It won't hurt anything.
Jon was right about the soap breaking the surface tension of the water. A good demonstration of it is to take a bowl and sprinkle it with pepper, then add on drop of soap to the bowl. Once the surface tension is broken by the soap, the pepper is 'pushed' to the edges of the bowl. That concludes todays lessons.
Good luck with getting rid of the mites. May their lives be short and their eggs wither and die.![]()