You guys might think I'm nuts, but you might give this a try...
For every season except hot summer, try wearing a base layer of very thin merino wool. Smartwool and Ibex both make thin 100% merino t shirts and long sleeve pullovers. Look for the terms "microweight" in Smartwool, and "woolies" for the Ibex. These things are magical! They are very soft and thin, machine washable and comfy, and they breathe. Sure you sweat into them, but it just doesn't get smelly...honest.
I used to wear polyesther leotard tops and cotton tops for years, and even without biking they were smelly after only a day's wear. I would never have believed how I can wear a merino shirt for maybe 4 or 5 times biking and sweating and it still has no underarm smell- I just hang it up to dry and air out at night. Pretty amazing. Something about the wool does not encourage bacteria growth. And it's the bacteria, not the actual sweat, that create the smell.
Perhaps you could wear one to work, change into a work top, and hang the merino somewhere discreet for the day to dry before wearing it back home again.
Just another suggestion instead of sudsing up in the sink or forever buying wipes...