The only likely risk is that the PSU could fall off and hit something.
Check the PSU to see if its case ground is tied to the black ground wires because with some PSUs they're kept separate (usually a sign of high quality), and if they are, then run two #18 AWG ground wires between the PSU case and the computer case (for a clear case run the wires from the PSU to the metal drive bay and also to a mobo ground).
Electrical tape isn't a very reliable insulator because it's so easy to pierce.