If you start trying to spot in small areas of finish without knowing exactly what the overall finish is, you could open a big box of weirdness, ie: linseed oil when the factory finish is clear lacquer, finishing oils when the original finish was straight linseed oil at the factory, etc. If it were mine I would just go straight to the wax and call it a day. Wax is compatible with anything.

"You can lead a man to logic, but you cannot make him think." Joe Harz
"Always certain, often right." Keith McCafferty