You'd need to continuity test the heating wire and the outer earth wire if there is one then you'd need to insulation test the wire using a 1000v mega tester. You might need to get a bit creative to mega test the insulation if the heater doesn't have an earth wire running inside it, the damaged area would need to be exposed.
Problem with heat shrink tubing is you'd need to cut the wire completely to get it on then rejoin afterwards.
If you damage UFH wires my best advice would be to get a sparky in who specialises or has lots of experience with UFH systems. This especially goes with UFH in a bathroom which is far more likely to give people a fatal shock if it's faulty.
If the rcd detected any irregularities it would trip the power. If there is anything problems with the ufh, this is far more likely to happen than someone meeting a shocking death (no pun intended) ufh controllers also monitor this and again will trip the power if there is a problem. It is highly unlikely for anyone to get an electric shock from ufh.
Even older fuse box's are likely to trip with irregular currents from ufh running through them.