How long is your commute?
Mine is 3-4 miles each way, and I get by okay with simply bringing a clean shirt to change into when I get to work.
I'm sweating profusely when I arrive. So I go into the bathroom and follow these steps:
1. Take wet shirt off
2. Fan & pat myself dry with wet shirt
3. Wash hands
4. Put on clean shirt.
5. Do not tuck in clean shirt until pants are completely dry.
That's it for me. I'm a little damp for the first 30 minutes of the day or so, but not bad enough for me to need to bring a dry pair of pants with me.
Another guy here commutes from further away, and he comes in full cycling gear and changes into work gear. Still no showers though.