How do I rewire an old light fixture?
Yes, just replace the wires. Even if you reverse the connections, the light will work. For safety's sake, make every effort to connect the wires properly. The silver screw should be connected to the neutral house wiring, white in US and Canada and blue or black nearly everywhere else. Try to confirm the silver screw connects to the outer metal sheath of the socket, the part with the threads. The yellow colored screw connects to the switched power of the house wiring and the center contact in the socket. The switched power house wire color is usually black or red in US and Canada and brown or some other color everywhere else. Just do not attempt to connect any wire with green (may be striped with yellow) or no insulation to either of these screws. Green or bare is for equipment grounding purposes and should be bonded to any metal components that do not carry current.

Strip the insulation from the wire ends no longer than necessary. Try to arrange the wire under the screw head to wrap almost full circle with no overlap. Wrap it in the direction of tightening the screw so the wrap is drawn tighter when tightening the screw. This only applies to binding post screws. If there is a separate hole for the wire and the screw acts like a set screw, then disregard this part. Replicate the connection methods used previously in the junction box, typically either wire nuts or set screw strips.

But please - whatever you do, turn the power off first!