New old Harmony Ukelele

My mother just gave me her old Harmony ukelele, I believe it’s from the early 1960s. The finish is flaking off and I wondered - if I first clean this with appropriate fine furniture cleaner, let dry, then VERY LIGHTLY sand the flakes down with a super fine grit sanding pad (it’s soft and flexible), then use a wood “food”/conditioner, will this do anything irreversibly bad to the instrument? I don’t know if there are special considerations for string instruments. I plan to have it professionally seen to later, but can not afford that now.

Thanks

Sorry, it seems the pics downsampled so much, you can’t see the texture of the finish well. If for some reason someone here is interested to see up close, my email is jlizkinsey@gmail.com

Most good hardware stores have a polish that is lemon orange oil, be sure to oil the fretboard as well.

If it were mine I might go with steel wool instead of sand paper first and see if that does the trick.