This is something you can DIY.........my aunt does it all the time. Google it and see if you feel comfortable trying it. I'm pretty sure it's OK since I see the parts with instructions in HD all the time. Just a thought : )

Why does the lamp need rewiring? It's easy if you know what you are doing. You must know what wire should be hot and what wire should be neutral.

saskatchewan girl, I would be willing to try as long as there would be a way to test the lamp without plugging it into a regular socket/cause a fire/etc.

texasred, I don't have an actual light yet. I want to get some vintage lamps, but they'd have old wiring. They might work, but I thought old wiring was unsafe, no?

My DH is pretty handy, though he has never rewired a lamp. He'd be up to helping me.

Some lamps may be more expensive to rewire than others, so there's no meaningful ballpark figure anyone can give you. There's a local hardware store in my town whose owner rewires lamps so cheaply I wonder how he even covers the cost of parts, but YMMV. Suffice it to say that this is way over on the easy end, on the scale of electrical task difficulty. Just get any old lamp at a thrift store, take it apart and see how it works.

If you look at the receptacles in your home you will note that they are polarized, that is one slot is slightly longer that the other. The neutral side of the receptacle is slighly longer that the hot side. If you have three slot receptacles with the ground hole at the bottom, the neutral slot is on the left.

Now, if you look at the lamp socket you will notice that one wire is soldered to the back of the socket. This is the hot side. The other wire is soldered to the side of the socket. This is the neutral. When you attach the wires to the plug, it is important that the hot wire from the back of the socket be attached to the smaller slot on the plug and the nuetral from the side of the socket be attached to the larger leg of the plug. This will keep the electrical current properly directed for safety.

If you are rewiring a lamp and need a new socket, you can purchase new ones at most hardware stores that have screw connections so you don't have to solder connections. Also, lamp cord is also available at most hardwares. You will notice that one side of the the cord is striped. This is the neutral side which is what connects to the side of the socket.

This is really the main issue to rewiring a lamp and once you get the hang of it you will be a pro.