How to Touch Up Wood Finish?

A small area of the window sill of a casement window has losed the finish. I would like to touch up the area. But I don't know which finish I should put on the areas because I don't know what is the finish on the window sill. I would like to find a way to determine the finish that is currently on the window sill. If this is not possible, I would like to know the next best way to touch up the areas without knowing what the finish currently on the window sill.
The wood might have been finished with some satin finish that has stain in it. The other possibility is that the stain was applied on the wood, and then satin finish was put on the wood. Both the satin finish and some of the stain has been weared off in a small area (by children playing on the window sill). For the stain, I can try to match the color. But I don't know what kind of satin finish that is.
I tried to put some Butcher's wax on the wood. But the wax actually dissolved the stain (or the satin finish that may have stain in it), and smeard the finish and made the look even worse than before. Is there a better way to determine what the finish was?
Thanks in advance for any info.
By the way, the finish must have been applied by the installer, and not by the casement window manufacturer because all the woods in the house have the same finish, and the manufacturer's Caring Instruction of the window doesn't say anything about restoring the finish.
Jay Chan

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