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