Something to consider is a GFCI is not going to prevent a shock just limit the duration of the shock, you will feel it before the GFCI opens the circuit.
If you feel you must go with a GFCI I would suggest using a GFCI breaker so the power in this up facing box is actually cut off instead of just the terminals of the outlet.
But as Bennie said you will have tripping if any water gets to the outlet.
A better solution is not to mop an open electric device.