I'd have thought that the risk of getting punctures was much higher and removing wheels, tyres and replacing tubes etc was much more likely to happen then simply unshipping a chain. Also got to ask, why did the chain unship it self? Sounds like poor maintenance/adjustment in the first place. A little bit of TLC would go a long way to prevent unshipped chains (a stitch in time etc). Gloves/wet wipes and a splash of water from your water bottle gets most of the dirt off your hands. I've also used grass/leaves in the past to clean my hands.