Once in college, someone stole my pants from the locker room once and I had to walk back to my dorm in super cold and windy weather in a winter coat and no pants. I got windburn on my legs. This was the late 90s and wind pants type things were acceptable to wear around, or perhaps even desired, since someone wanted mine so bad they snatched them. I think the culprit was someone I knew, as she complemented my pants the prior week and then was wearing identical ones a week after the theft. I never did ask her about it, but come on?! They were currently in stores so it's possible she bought them.
Anyway, my suggestion is wind pants. The trick is to put them (or any pants when you are kinda damp) on like pantyhose. Scrunch them up, stick a foot through, and unscrunch them on your way up the leg. You do have to sit down for this. Dry your top half off, put hair up in a clip to prevent drips, then put your towel around your waist. Dress your top first. Put your shoes and socks near a bench, then sit on a bench- on the towel to avoid public icky-ness. Use the inside of the towel that has not touched the bench to dry off your legs and then your feet. Put socks on, then you are free to step into your shoes while you put on your underwear. Then work the pants up most of each leg. Then you can actually put your feet totally in your shoes, stand up, and pull the pants up the rest of the way. Then you can grab your flip flops and put the gross soles together and deposit them into whatever section of you bag is designated for grossness. Procedural overkill? Maybe. But it works for me. I'm not really germophobe, I will 5-second rule my dropped food all the time. I just think locker rooms are particularly icky.