I've never seen a transmission pan develop varnish on the inside.
I've always just used the power washer (yep, plain water) then let air dry. I worked at a transmission shop in the late 80's - just a power washer was used for all cleaning jobs.
Varsol, Stoddard Solvent or plain old mineral spirits. Kerosene will work just as well. If you have anything more than residual ATF deposits, you have a problem or lack of ATF drain/refill (which is all you need).