More important, is the veneer modern. In recent years a lot of veneer is made with a paper back which is stuck to the wood with hot melt glue. The hot melt glue will strip a lot easier than the urethane. If it is an antique you would be safe in that the veneer is applied with either a resin or hyde glue and would be safe to strip.
Personally I think elbow grease is toxic. Urethane is chemical resistant anyway. If you use something mild like citristrip your looking at a lot of work. It's much more toxic but I would use a methylene chloride remover. For a urethane finish I would use Kleen Strip remover. You apply a liberal coat and let it soak for 15 to 30 minutes keeping it wet with stripper. Then with a broad knife scrape off the finish and residue. If it has a lot of detail like moldings or carvings a brass brush is helpful. Once you start scraping you need to work fast because air is getting to it and it's trying to dry back on. Then to rinse what is left I use a power washer that only has 1500 psi to rinse it with. Some other models of power washers have the means to adjust the pressure so if you can turn it down to where you can almost spray your hand without hurting you it would be fine. Another method is to rinse the residue off with lacquer thinner. It needs repeated rinsing changing rags because the residue contains wax which can interfere with the new finish.