Until a recent change in departments, I was in a public-facing customer service position. I know what you mean about not looking or smelling homeless at work.

I'm also very sweaty. I come from the same genetic stock as Rodney Dangerfield. Even sitting at my desk in the A/C I'm always oozing something from somewhere.

Here's what works for me:

1. Shower very last thing before leaving home. Apply deodorant. (I'm allergic to the stuff in antiperspirants.)
2. Wear clean cycling kit. Not clean as in "doesn't smell too bad", but clean as in "freshly laundered, unworn". None of this "wear work clothes" works for me. See Rodney Dangerfield, above.
3. Arrive a half-hour before shift start. Cool down in the back. It takes me 15-20 minutes to cool down sufficiently.
4. Birdbath in the staff men's room sink. Face, neck, arms, pits, chest. I keep real cloth towels at work (Rotated home twice weekly), but use the anti-bacterial hand soap from the dispenser.
5. Dry off. Apply deodorant. Put on work duds, wipe down sink area so co-workers don't complain.
6. Hang towel and cycling kit in locker to dry.
7. Step out on the floor, fresh as a daisy for work.

In ten years of bike commuting, never a peep from patrons, co-workers or management.