Which is easier to replace, the stone or the little woman?
They do have dripless candles.
I don't know of a process that will extricate wax from stone.
Ron

My understanding is that Bath Stone is a Limestone mined in Bath England.

One cheap and it wont hurt to try option.

Take some baking soda and mix it with a small amount of water to make a thick paste (a poultice) and spread it thick on a test section on the level section of the ledge. I would just try a quarter size dot in the middle of a dark section.

Candles have oil in them, as the poultice drys it will pull the oils out. Leave it alone for a day to ensure it is dry all the way. When it is fully dry, brush it off. Is the stone lighter in that spot than the surrounding area? If so, do it all over the stain, you might need to repeat a number of times and it might never be the same but it might help.

Another option after trying that. Wet the stone next to the stain. Does that help to blend in the wax stain? If so, buy a bottle of mineral oil from the pharmacy and rub that into the stone. That is how you maintain stone kitchen counters.

What if you took a terry-cloth wash cloth and laid it over the waxed area and held a clothes iron on it?

Would the wax/oil liquefy enough to get wicked into the cloth towel?

I have successfully gotten wax out of carpet this way.

Hi everyone..Easy thing to try with candle wax is to spread some dry powdered cement over the stained area. Then take a heat gun or hair drier and warm the area to melt the wax residue. It will flow thru capillary action towards the dry cement and be absorbed. You may have to do this several times. Just lightly wire brush the area after vacuuming the powder residue...it should look much better. Good luck, Mark in Buffalo