Riding slow/easy to avoid sweating was never an option for me either.
It's not just sweat either - it's salt, dead bugs, road splat, dust/dirt that feels sticky and gritty like sandpaper when dry.

I have had excellent results with bird-bath cleanups in a restroom. It was made MUCH easier since I could stash a clean-up kit at my desk which was about 50' away from the bathroom; and I could hang up soggy stuff to dry.
Rest in the shade and drink water until you quit sweating.
Brought minimal toiletries in small (refilled) travel-size containers.
Sink shampoo - cold water on your neck cools you off quickly and feels wonderful on a sweaty ride
Use plain clear dial anti-bacterial liquid hand soap - just a LITTLE bit on a wet washrag. Scrub down EVERYWHERE (handicap stall gives you manuevering room/privacy)
Then use a 2nd wet washrag to wipe down with (removes most soap residue)
Towel off with travel-thickness microfiber towel
Wipe between toes with alcohol-based hand sanitizer gel
Apply antiperspirant and put on clean clothes, finger-comb hair.
Clean up the area so nobody complains ! That includes any hair in the sink or splashes.