Remember not to sand the veneer. That would remove any natural patina the wood has.
After washing your pieces well of any stripper residue with laquer thinner. Make sure to allow enough time for the wood to dry out. The one time I ignored this the new finish developed hairline cracks.
A good replacement finish is catalized laquer. It is really tough and will present a nice finish with many coats. You may have to rub it out a little of course. It also should not tend to dry out and crack. You see this finish commonly on wooden kitchen/dining room tables in the last few years as it also does not become stickey or break down easily.
I personally do not thing urathane finishes with no hardeners are a good ideal. Yet everyone to there own inclinations. It also never hurts to get a piece from a junk car and do it first to see if your expectations are met.