Refinishing advice for old wanlnut(?) table with peg divots

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I have an old table, The table used to have some very damaged lacquer on it. I stripped off the lacquer with citrusstrip, and the surface looks pretty good.

I noticed three recessed plug-holes on the surface where I can feel the other ends of dowels/pegs sticking out of the bottom surface. Since the pegs go all the way through, I think it was some sort of original fill that maybe had/has putty or glue on top.

The table is 28.75 x 49.5x0.75", perhaps walnut? Top made from two edge-glued boards, probably pegged, since the rest of the construction is pegged. Slotted wood screws hold the top to the skirt. It looks pretty old.

Because it is an heirloom from my wife's mother, I do not want to do too much more processing to the top surface. I was wondering how to fill the divots. I do not want to try to pound the pegs further up through the holes, since they might be glued and might lift the edges of the through holes. Since my wife grew up with the table and has memories, I don't want to mess with it too much, but she'd like a modern finish without susceptibility to water rings.

My two questions are:

* How should I fill the three shallow holes (each ~1/32" deep, ~3/8" dia)

* What finish do you recommend?

Thanks

I would fill them with a coloured wax stick.

You should watch a few of Thomas Johnson’s Antique Restoration videos on Youtube before making a decision on finishing. He’s in Maine, so the products he uses will be easily obtainable for you.