Tara, it's hard to know how to advise someone without knowing their level of experience or aptitude to the task.
Mark's suggestion of using a card scraper is a good one but, if you have no practice in using one, you could seriously damage the veneer. Don's question about using a stripper and places where the veneer has raised is a good one. Liquids, such as stripper, could wrinkle raised veneer. This can be fixed, but it takes some level of expertise and the right tools.
If you feel competent to tackle the job and have the right tools you should be good to go but, if you lack the experience, perhaps you should let a professional handle it. You were astute to ask for advice as there are, surely, ways a project like this can go wrong on a rare piece of furniture.
Think about how you'll remove the old finish. Think about how you'll make repairs and prepare the surface for the new finish. Think about what type of finish you want to apply and how you'll do it.