RJ,
Hyde glue needs to heated in a glue pot so you may be looking at having to invest in some tools just to do this one repair. I have sucessfully tacked down lifted veneer with both PVA glue and super glue (I am not even going to attempt to spell sianoacrylate

)
The secret to success regardless on what approach you take is to have clean surfaces to glue. Often with old hyde glue the glue breaks down and crumbles and there is nothing for the glue to bond to. When this is the case I carfully try and slide a small piece of sandpapper between and work some of the crud out and give each surface some tooth.
I couldn't tell from your description if the lifted veneer is along a seam in the field or at the bottom edge. Any glue you put between the veneer and substrate will squeeze out when you clamp it so besure you don't allow it to dry on the surface.
Can you attach a picture of the lifted veneer?