Well since you have a Dell and most of the advice givers don't I'll tell you what I did. I put more memory into my Dell Dimension 8100 and as you have surmised the power supply must be swung up and out of the way for access so all the tips to leave it plugged in are pointless. Just shut everything down, unplug the power cord from the back of the PC, remove your case, attach your wrist strap to your wrist and the clip to bare metal of the case somewhere that it's not in your way, swing the power supply up and out of the way using the release mechanism and do what you have to do. Make sure when you put the power supply back in position that all your wiring is safe and away from sharp edges.

I don't even have a wrist strap and accomplished it by simply making sure one hand or arm touched the metal case the whole time I was in there. :-)