I would just get a marble or stone piece cut, and not refinish it.

I want to refinish it. I am not clear about why you would suggest getting a piece of stone cut to cover the entire top. Though I am guessing it was originally used (or misused) as a plant stand, I do not plan to use it as one once it is completed.

Thanks, Handymac!
I have both denatured alchol and lacquer thinner on hand. I do hope it is
shellac as it might be less messy to remove than if I have to use stripper.

When it is time
to apply a new finish…I don’t have much use for shellac currently. I have made
it before (some years back) but I’m not sure I still have the flakes. The local
woodworking store closed.

If I use another
finish/varnish, is the color likely to turn out very different than if I use
shellac? After all, I only need to strip the top. The sideas are all ok. The
whole piece has kind of a golden color, but I think that is just because it is
old wood rather than being stained that color. Other old oak pieces I have
stripped in the past looked very golden even though I did not stain and used a
clear varnish. I was thinking about just thinning some poly and wiping on
several coats, if that is not sacriligious.

There are several different colors of shellac, so that is also a factor.

You can use a wipe on poly and even tint it(can purchase tints on line since the store closed).

It will probably look different no matter what you do---matching a finish is actually a real skill. The advantage of using shellac to experiment is how easily it can be removed. Poly cannot be removed using thinners, you have to use a stripper.

This project is a really good way to experiment with trying to get close, if you enjoy the trip.

it looks like from the photo that there is a piece of wood that lifts out of the center of the table. I am suggesting replacing that with a stone product, otherwise the finish on the table looks good.

Thanks
again, handymac. Once I have it stripped I will be able to assess. Maybe I’ll
stain lightly and carefully until I get it to a shade lighter than the rest,
before the varnish.

Yes, sloyder, there was
originally a panel of flimsy wood covered with tattered velvet in the center. I
have already cut a square of green marble to fit in the recess. Just have to
bevel the edges and polish them, as it projects up from the recess.

Mac is giving good advice. Concurning your handi-cap,I've had to adapt and improvise in order to stay in the game. Quility suffers but I can't give in or give up. On large flat surfaces I use a drywall sanding pole which alows useing both hands and putting some body weight into sanding. Covering handle with foam pipe insulation tubes increased size and made handle soft making for better grip. If you are lucky the old shellac will amalgamate with the alcohol and damage disappears. If you see that happening be aware that most modern finishes like being applied over shellac. There's no need to totally remove old shellac,just smooth it out,lightly sand and top coat.