If the power supply has been sitting around it should have self discharged. Bleeder resistors are standard practice, even on cheap supplies, though it does't hurt to be careful. Dead shorting a capacitor probably isn't going to damage it, I've done it many a time, but for some types it might not be as good as a slightly more controlled discharge. Just attach a wire to ground and put a 10k resistor or so in series with it, perhaps attached to something like a screw driver, attach another one directly to ground. Apply one to one lead and one to the other of the cap for a few seconds, then dead short the two leads. The 10k resistor will do a low current controlled discharge (really large caps just hold it there longer) and then the dead short will bleed off the rest. though remember large value high voltage electrolytics tend to slightly recharge themselves from dielectric absorption, at the same time however the leakage on caps like that will cause them to self discharge over time. I wouldn't be so paranoid over it unless you're working with TV tubes, which upon pain of death should be discharged carefully even after sitting for extended periods of time.
Aside from that the only tip I can offer you is get yourself a decent temperature controlled soldering iron (MPJA.COM has several inexpensive ones) as soon as you can afford it. And for bulk desoldering your absolute best investment is a heat gun, which you can pick up at most DIY store for 20-40 bucks. Variable heat control would be awesome but a low and high setting are fine. You can make your own custom tips using thin sheet metal, scissors and a ltitle sand paper to deburr the edges, you can desolder just about anything with that and a pair of plyers, and learning to control the distance you hold the heat gun from the board. Low heat to preheat then high heat for a few seconds while applying pressure with the plyers. SMD components will tend to just fall or get blown off by the airflow.