Good points above. I had good success with birdbath cleanups after arriving at work red-faced sweat-slimed and all gritty with salt, road grit, and dead bug-splat.
First, cool down until you quit sweating. Drink water, seek shade, relax.
Do a cold water sink shampoo fully-attired (if your hair is sweaty). Clean the neck and face even if you decide not to shampoo. This is much easier if it's a handicap sink where you can fit your head under the faucet spout. Otherwise you may need a cup to pour water over your head.
Finish in a handicap restroom stall. Strip all clothes off for thorough cleanup.
I kept a small bucket at work, about a gallon. Filled it with clean water from the sink. I also kept two washrags and a big towel at work.
I would put a very small amount of liquid anti-bacterial hand soap (eg: dial) on one damp washrag. Use the soapy washrag to wipe every inch of skin that you didn't get at the sink.
Start at the top and work your way down. Some areas may need scrubbing.
Then use the bucket to dampen the 2nd washrag to wipe down as your "rinse". Wring out the rinse rag over the toilet every so often, then re-dampen the washrag with the clean water in the bucket. It may take a few passes to get all soap residue off.
Dry off with big towel. Apply toiletries. Dress. Completely clean the washrags. Clean up any drips and splashes including mirrors and floors.
I kept a second set of towels+washrags so each day I had a dry set of linens.
I also found that sham-wows can help hair get less damp so it will air dry faster. Use the sham-wow for a final toweling pass on your hair and toussle it a bit. My office was deserted and the damp hair wasn't noticeable anyhow.
This routine was actually faster than a shower since there's no temptation to dawdle; and it provided equivalent results. The restroom was 1 minute from my desk.