You could wash in clean water sources like in vaults or one of those clean basins (i.e near goodsprings), or create a menu at dirty water sources asking you if you want to drink it or add detergent and wash yourself (will give off radiation). Or just combine a bottle of dirty (will give off radiation) or clean water with detergent and use the resulting soap.
I think it would add to the realism. Theres a lot of trash, dirt and blood in the wasteland. Smelling really bad in real life would impair your social skills.