Do you actually want to clean them or just move the dirt around? You wont get the tires what I would call clean without some kind of cleaning solution and anything water based will take forever to dry out of the tire.

Lighter fluid for flick lighters has nearly no smell, but the Ronsol and Zippo fuel is expensive. The charcoal grill fluid smells a bit because it's less refined but you can get a liter of it for less than a 100ml bottle of the good stuff.