I used to get an extra pair of hands and providing there's enough room I'd undo both sides and get my help to put force on the side I did first to stop / slow down the leak and then quickly do the other side and stick a finger or thumb over the exit points and flip the rad 180 so the water didn't come out.... after either shutting down the valves or on old dodgy systems i'd freeze the pipes and then fit a stop end on the valve... where possible.
Stat valves are ok turned off providing you dont end up with a cold room as they'll kick in on their frost setting which is usually the lowest setting, which is not quite off.
Although i'm not a plumber so listen to Uggy and McP
I did used to get wet and need a few towels in most cases.