I don't have a shower at work but this is what I do...
Shower in the morning, use baby powder for the groin, I pack my work clothes and not wear them. When I get to work there's a seperate handicap restroom here with it's own sink. I go in there and immediatly take off my shirt to cool down. I damp a wash cloth and wipe off the sweat. I wet my hands and run them through my hair. I dry off using paper towels and put on more deoderant. When I'm dry I change into my work clothes. It takes a little while but the ladies here have never complained. And they're the type who would if I did stink.
Mainly if I still feel like I'm sweating I wont put on my work clothes. I'll just re-wipe myself down with the damp washcloth.