Start small, do something in the bathroom that will easily wash away, leave no evidence (such as splats on the wall or clothes in the washing machine).
You can start off with some thinker such as methlycellulose add a little white poster paint along with the color of your choice of poster paint. Use that and shower off with your clothes on and most of it comes off.
If you do your own laundry (helps a lot with this) you can just throw the wet clothes in with it and the rest cleans out.
Don't use any gunge which is lumpy and difficult to wash down a drain. Stick to stuff like shaving foam, custard, semolina - though have a plan for how to remove and dispose of any packaging.
Stick to doing stuff in the bathroom - lockable door, and you have everything you need to clean up (including flushable toilet roll).
If you want to wear clothes, perhaps stick to swimwear - swimming shorts or trunks - as these will dry fairly quickly and naturally, provided you can find somewhere inconspicious to put them in the meantime.
If you wanted to wear other clothes, consider using old clothes which would otherwise be thrown away. You can mess them up, then tie them up in a plastic bag and throw them straight out into your wheely bin.
GungeMad said: Start small, do something in the bathroom that will easily wash away, leave no evidence (such as splats on the wall or clothes in the washing machine).
Obviously do it when they aren't there.
Co-sign also be sure to be or close to warm water not just for clean up but so you don't get so cold depending an what substances your working with.