Double-check with denatured alcohol just to make certain it is not shellac. If it is, it should dissolve easily.
If not, it is probably a spar type varnish (not a polyurethane, but it could be -- you never know for certain).
Try mineral spirits with grade medium or finer steel wool or with ScotchBrite type stripper pads. This should remove the old finish while dissolving it and in effect allowing it to re-coat the wood. Go lightly at first. The more you rub, the more finish will be removed and the lighter the finish will become. Try to be consistent so the woodwork will all be the same shade. High spots on moldings may become lighter and grooves will be darker unless you change your technique accordingly.
You can wipe the wet surface with paper towels or a rag. Use a small metal bucket for the mineral spirits.
If the mineral spirits don't work, you may have to try something more aggressive but milder than a stripper. Talk to your paint store.
The finish may be fine after you do this. If you need more protection, you can try a tung oil with a high solids content but I suggest using a combination oil/polyurethane wipe-on finish or a poly wipe-on finish. If you use tung oil the finish may have to be renewed every few years. :-(