I shower at home. Ride pretty hard to work. Wipe down with one of those super absorbent towels and change. I live in Atlanta (as in HotLanta) it's just a little humid here. Have ridden over a year doing this. No problems at work. the Shamwow towels (and products like it) are small but very absorbent. Space in pannier is a premium. I am not affiliated with the product just happy using them.

I started out using baby wipes, then I heard about Rocket Shower. IMO Rocket Shower is vastly superior to the baby wipes. With the baby wipes I felt slimy after I used them. With Rocket Shower, I feel cooled and refreshed. I also use a home made dry shampoo because I have long hair.

When I was in college, I learned to carry some deodorant powder (like Shower to Shower), wipe off in the bathroom sprinkle a little here and there and sometimes put a fresh shirt on. I'd refill a small seasoning bottle with a shaker top to make it more convenient to carry.

I have to enjoy it while I can; we're moving to a new location at the end of the year and the best I can hope for is that they'll put a bike rack in the parking garage. It may end up outside. They'll do whatever they want and hide behind the excuse of "the property company sez we have to do it this way." I hold out a little hope in that the site manager is kind of a fit guy and is well aware that I ride my bike most of the time. I lobbied for a shower but didn't get it. Maybe as a consolation prize they'll put the bike rack under cover in the parking garage.

I was using Shower to Shower brand, and when I got home the wife would say I smelled bad. I switched to good ol' fashioned baby powder and now she thinks I smell kind of fresh once I stop sweating. YMMV.

well so far here's my list if I'm going to commute to work:
Wipes (it sounds like the brand really isn't all that important to the majority of people)
baby powder
a set of clothes for riding, and a complete different set of clothes (underwear, socks, etc..) for work.
Deodorant, and some sort of body spray / deodorant (maybe in place of the baby powder?)

I don't ride clipless pedals so I would be wearing regular shoes.
I have an old pair that I typically toss on while riding, and then a different pair that I use for work.
Would it be worth it swap out shoes as well?

I ride in work boots or in hiking boots, both of which I can wear to work. (I have bad ankles, and the support helps when walking.) However, I use toe clips and straps, which tend to scuff up the shoes a bit.

If you use platforms without clips or straps, you may be fine in ordinary shoes or sneakers. How long is your commute?

I have just regular platform pedals with no straps or clips.
the commute one way is about 5 miles, but I think I can find a way to lengthen it a bit after I get more comfortable.

Evaporative cooling air shower:

Desk fan, rubbing alcohol, spray bottle.