Unless the lamp holder needs to be replaced, a trip to your local hardware store to buy a length of lamp cord and a plug is usually all you need. 20 year old wire is probably ok. Just bend it to make sure it's pliable and can be tied into a knot like many lamps do to keep the wire from pulling out.

I would use a new cord for your old lamp. The old extension cords may be OK to use as extension cords, but if they ever give you trouble, discard them.

I have rewired a few lamps. I got the new cord and socket from home Depot. Utube videos offer good instructions.

You folks are awesome, thank you so much!

🤗