Old English is a liquid furniture polish and scratch cover-up. It should be where the furniture polish is. The wax sticks are about the size of a crayon and they come in different colors to approximate finish colors. They should be where the refinishing/stain supplies are. Ask your hardware person. They should know if they have these items and where they are in the store.
If you have 60s-70s finish on that end table, more than likely it has some type of opaque, sprayed finish on mediocre wood. Refinishing it may not be prudent. I would not refinish that end table. Too much work for little return.
I agree with you, at the corners it almost looks like a fine layer of "something" is off. In this case, if I want to just spruce it up, what should I do? Can I apply the shellac after mild scrubbing with extra fine steel wool? Can I apply the "wipe on poly" on shellac to give a shiny finish or will it ruin it?
Thanks.