I wear my gym shirt while bicycling which I sweat into profusely. I get to work and lock myself in the family bathroom, where I take my gym shirt off. Then, I take out a linen towel I bought that packs super tiny, get it wet, and wipe down. I stand and cool and dry off for a bit, then put on the shirt I packed. The linen towel gets a soapy wash in the sink and then wronged out. Then, towel and gym shirt get hanged on hooks in the office near a window (as far as I can tell there's no bad smell and I have explicitly asked others in the office) and both are dry within a couple hours.
Change into gym shirt after work and bike home, take a shower.
It's a process but it's worth it, I've lost 7 pounds without much else lifestyle change.
The linen towel is fairly critical - packs small, light, dries quick and is odorless (allegedly linen is anti bacterial). They're also great for travel in general.
This however is precisely why I have some ebikes in addition to human steam powered ones - its so nice for commute or journeys when you want to arrive feeling refreshed but not need a shower or change of clothes.