Can you desolder it so you don't shorten the wire too much?

Depends, are you planning to reuse the sockets or replace them?
If reusing cut where the wire is soldered to the tin lead and work the staples up just enough to slide the wires out, this way you can slide them back under the staples and push them back in.
If replacing cut them at the bend where they come through the PF and do the same thing for the new ones.

If you can pull the leads out from under the staples, you should cut it far from the lamp, which will give you more room to work. If you can't, cut it at the first staple, and be prepared for some burn marks if you're not careful.

I'm replacing here. I don't see any slack that would enable me to cut them where they come through at the playfield. Also, if I cut the news one at the same spot, how to I re-attach? Solder?

Yes, feed through and cut a little longer overlap and solder.
I like to lift the staples a little and slide the new legs back to the braided wire where possible then push the staples back in with a punch.
You can also use short wood screws and washers to secure the leads if you can't get a staple in there.

If I'm lifting the staples, why not just pull the whole thing out? (Noob here).

ideally your replacing it with a better design
http://www.marcospecialties.com/pinball-parts/24-8776

and if your keeping the existing just desolder it, if you have to clip anything your gonna have to "hack" in new wires anyway as you just cut it too short.

its easy but not "Fast" work.

You can do that but the tin leads have to be straightened and all the solder removed from the end to pull it through the pop body.
I always replace the socket and cut the lead in sections so I can fold it and use it to lift the staple.
If it is too tight and no room to work overlapping and soldering works but where possible I like to go full tin lead back to the braided wire.

Basically, I was replacing the bulb, and the plastic housing around the lamp socket broke apart. I cleaned out the broken plastic housing, and now all that's left are the 2 metal "sockets" which aren't study enough now to accept a bulb. I assume I'll have to replace the whole lamp...just wanted to figure out the best way to do it, without taking the damn Pop apart....