nice lamp.
are there screws to terminate the wires in the socket ? if so replace with new wire. if you want cloth covered old looking wire , its available. if you must join the wires you can cut them to 2 inches , strip the rotten rubber, slip on 1 1/2" of heat shrink instead. then shrink it . it comes in 3 foot lengths and in various sizes and colors. some of it has sticky stuff. Use a bic lighter to shrink them down.
slip heat shrink over the long wires , then solder them , then pull the heat shrink over the connection and the heat shrink that you used to insulate the 2 inch wires previously.
do a western union splice like this
http://www.thumpertalk.com/uploads/mont ... 658639.gifif that link is bad just search for "western union splice"
this way you'll have a good safe connection and new wire. the connection won't make a lump in the wire and it won't ever fail.
when you connect the plug, make sure to use the kind with one spade bigger ( a polarized plug) the small prong should connect to the small bump on the light bulb (not the socket threads) if you don't use a polarized plug and re-use an old one if anyone touches the threaded part of the socket they can get a shock so don't do it that way although yes it'll still light the bulb.
if you have a switch on the lamp , always switch the hot wire. it's the one to the smaller prong on the socket and if wires are colored normally it's the black wire but there are often exceptions in color.
in normal wiring the black is hot, but normally the electrician will run wires to the lamp pot in the ceiling and then there will be wires to the switch. of course both wires are needed , the black and the white are both hot in this instance and a good electrician will wrap colored tape on these wires to signify they are both hot wires. If that doesn't make sense then just be aware when working on lighting that it's not uncommon to find white wires that are hot and not neutral so be wary of that, but it's more to do with house wiring than lamp wiring.
lamp cord that isn't color coded always has a bump on one wire to differentiate the two.
if you need to tie a knot to restrain the wire as it passes through a hole in the lamp then use a UL knot or (underwriters knot ) like this:
http://image.slidesharecdn.com/kto12ele ... 1377136178don't use wire crimps, although they can be ok if done right , so often they aren't and you don't need them, a proper soldered joint is much safer and less bulky.
inside the electrical box if the lamp is permanently connected ( hard wired not plugged in) then there I would use electrical "wire nuts" or "Marettes" wrap them with tape to keep them from being able to accidentally pull off the wire. making soldered joints in the box might not break code but if you want to change the lamp you won't need to deal with soldering wires. so use the wire nuts there but use the appropriate size for the wire, usually the orange ones.
or maybe it just helps me realize that I'm doing this stuff for personal satisfaction and not just monetary gain. 
