Hello Peter
If you have any old bits of walnut wood, you can sand it down, catch the dust and mix it with PVA glue (the white woodworking glue)..
Mix it to a stiff paste then press it in to the holes and let it set, it can be rubbed down too..
If the holes are big, you may be better drilling a hole and making walnut dowels to glue and tap in..
Cheers, John