It may just need a clean out.
If the harmonica is held together with bolts or screws, use a fine screwdriver to dismantle it carefully, laying everything out so you can reverse the process afterwards.
Brush gently with an old toothbrush, being careful not to damage the reeds. Use tap water at first.

Whatever cleaning agent you use subsequently, remember you're going to breath the vapour and taste the residue after.

Splott Man