The tissues of the arms and the legs could not be able to survive without the blood and oxygen supply which are essential for every tissue or organs to remain healthy and perform different actions.
Experiments on animals suggest that 3 hours or more without a continuous blood supply will initiate significant changes in tissues of the arm and the leg. Minor changes start to occur after 40 minutes but major histological damage takes place after 3 hours or more.
Fingerprints are still recoverable for long lengths of time, about 6 weeks, so you would still have the fingerprint ( no DNA profiling ) so you would likely be fine if it wasn't there for long.
