You can easily join the PSU's without 'cutting' wires.

Instead of 'cutting' them, just strip off a bit of the plastic insulation
and either twist them directly together (not so secure), or twist/solder
another piece of insulated wire between them as a bridge(better option).
Or even twist them together AND twist more (spare un-insulated) wire around
that joint for structural strength, and solder/tape it all up. (preferred solution)

That way, when you are done, just un-twist / un-solder the wires and tape over
the area where you stripped off the insulation. NEARLY as good as new, and NO cutting.