How safe is to work on an ATX PSU as a bench power supply?
Will I then risk something by touching/soldering the wires after shutting it down again?


Hm, the output side of your supply should generally be safe for touching,  because it's low voltage.

But:

When cutting multiple wires at once, you might create a short on the output, which might discharged a charged capacitor in very short time. That can damage tools (think welded "holes" in cutter blades), can cause arcs (and thus possibly cause eye damage or fire). Nothing too criticial, just be a bit careful when cutting without making sure capacitors are discharged first.