Put outputs of 2 computer power supplies in series?
It all comes down to one simple issue.  Is the ground (black wires) of the second computer power supply connected to mains power input green-wire safety ground, or is it not connected?  

It should be trivial to actually measure this with a cheap meter or even a battery and light conductivity tester.  Or even by opening the power supply unit and examining how the green-wire mains safety ground is handled with respect to the power supply black-wire ground node.

If the mains green-wire ground and the output black-wire ground are connected together then you cannot use the power supply in a "floating" configuration as you are proposing.

This assumes that you are using the computer power supplies properly with a grounded mains power cords. Improperly disconnecting the green-wire ground is a safety hazard at best, and likely illegal in a school or other public building setting.