Neither would be my choice of finishes to restore this table.

The problem with your "natural route" is that coconut oil is "non-drying" ... it gets gummy and collects dirt. Like the spot in your cabinet where the bottle of salad or olive oil sits.

Yes, it looks good for a bit.

Beeswax will oxidise and blacken, leaving you with a table with gummy, dirty and/or black spots where the original finish was worn off.

Is that what you want?

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Your problem now is that you worked "some" in and it's going to affect anything else you do because it soaked into the wood.

Not much will stick to oily wood, so you now have the problem of removing the coconut oil with something that's capable of dissolving it ... mineral spirits or turpentine or alcohol are the least obnoxious.

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The classic "beeswax finish" uses 1/3 raw linseed oil, 1/3 grated beeswax and 1/3 turpentine. The linseed oil will dry although the beeswax still will blacken. It's what gives the old oak furniture it's dark "Jacobean oak" look.

The steps will be:

1 - Sand lightly to remove the old finish and smooth the splinters
2 - Clean the coconut oil crud off with mineral spirits
3 - Apply the beeswax/linseed/turpentine finish