Here in Thailand, all the 7-11's sell these wet cloths, packed in plastic. The material is a terry cloth like an american wash cloth. The wet cloth is impregnated with a light cologne scent. There are 2 sizes, and the larger size (24 baht, about 75 cents) is perfect for clean up after a run.
This is no problem!! I have done it in Florida many times.
Basically, just go into any restroom with a sink--preferably one with the sink in a private stall (handicapped stalls work well for this situation--or some office buildings have one room restrooms where you lock the door and the sink is included in the locked area--this is what you need).
Take off sweaty running clothes. Turn on water. Splash water all over your body, everywhere (yes you will get floor wet, but who cares? They are made of tile this isn't a big deal). Now put soap in water, lather up your hands, and wash everywhere, quickly (maybe not as thorough as if at home but as well as you want--you will get the hang of how much you want/need). Now comes the messiest part--again splash water all over your body from the sink (cupping water in your hands obviously). More water will be getting on the floor, but again who cares. Get all soap off. You have just showered.
Now, obviously, dry yourself off. We are used to sweating in Fl after runs--this isn't a big deal you will feel clean just like you showered at home after running in Fl and then got dressed at home.
If you are in relatively clean office (esp. if this is where you work), take towel from bag and dry floor. Or bring old second towel for this purpose. I've also left the floor wet at places like outdoor parks and/or McDonald's--they usually have a drain in the floor and I figure the water will dry and they will clean it (the nasty factor makes me not want to use towel in these situations).
I've done this at away races, again if outdoor nasty restroom then I don't clean floor. And I've done at an office where I worked--at which time I did clean the floor esp b/c co-workers would come and see wet mess.
The key is that you have to find a bathroom with the sink inside the locked area. This might take a little looking but they are around pretty much everywhere.
The hardest part for women is our hair--not very easy to do your hair in this situation and make it look decent. I would just run my fingers with water through my hair a little--then put back with a clip for the afternoon. For men, this should be much less of an issue (which is why you guys have it so much easier!!)
I always felt great after these showers--honestly just like a real shower!!
Well, I havent tried this but I've thought about something that's a variation of some of the above posts.
Shaving your head would be a great idea. No need to try to make your hair look good...I used to use gels but the dissipating heat always melts them...so go bald (it also makes it much easier to keep body heat down).
Step 1: The shower
I'm thinking coffee can + washcloth or giant sponge. Fill coffee can with water, use sponge or washcloth #1 without soap to wipe your body with water. Apply liquid soap to sponge or washcloth #2, dip in water, wash yourself. Wring out sponge, dump can and refill, then rinse as necessary to wash soap off. Dry off. Apply cologne, deodorant and/or whatever.
Step 2: Cooling off and killing the sweats
Soak large bath towel in very cold water. Wring out the towel so that it does not get you wet. Drape towel around your neck & shoulders where it will apply substantial cooling to your upper body and absorb sweat which runs off your forehead and down your face. Keep cold towel on you until your body temp comes down. A second towel across the thighs may be necessary or a hand towel draped over your head. Wait 10 minutes or so.
Step 3: Dry off again and put on clothes
Step 4: Go to work, perhaps with a cold hand towel to apply to your head as needed.
About the time I came up with this they put a shower in where I work...then I also quit running. I am now in a situation where I would need something like this and I am curious how it will work. If anyone tries it, please post back (I am getting ready to un-quit running but have no time for it unless I can master a stealth shower method like this).
Just get yourself something like this, there are lots of different models:
You can either use it in a bathroom with a drain or outside. You really only need to wash your pits, face and maybe your feet to be relatively stink free.
Ran for years with no showers available. This was at lunch time.
Ran my workout. If there was a bathroom available I just wet toweled down after the run using a corner of the towel, dried off and changed into my work stuff. Went back to work.
Showered in the morning or evening.
Training was more important than showering after the workout. I just made sure I showered sometime during the day.
In the women's cosmetics section of big drug stores, they sell cleansing wipes for the face. This also works for pits, crotch, and feet. Use it.
Another thing is before you go out, make sure you shower the night before and put on STRONG deoderant. This is key. You might want to put it on after running also (I don't) but the key is to do it BEFORE you even start to sweat. I have a problem in the summer with feet/sandals so I also put on some feet balm/deorderant. Powder might also work. Sprays work.
I'm female so I wear my hair back in a pony tail and tuck the end back in the hair hand. After I brush my hair, stick my head under the hand dryer and then put it back up in a pony tail. No problem.
My work has a supermarket next door so sometimes I go to the frozen section to cool off in a hurry for just a few minutes. It works!
I've been running doubles for years and only shower once a day. My co-workers kind of think it's strange when they realize that I am not showering after running to work, but I look OK and really I don't care that much. Bosses have never had a problem with it. Some co-workers do think I'm weird when they find out that I run more than just to/from work, like 20 milers on the weekend, but I try to keep that hidden. ;)
I often commute by bicycle to and from work and my problems are similar to the op's. A complete change of clothing, including underwear, a wet towel wiping down face, armpits, and crotch, body spray, and deoderant. That and I shower like a made man before and after work.