I don't know of anyone who offers precut pieces, but I do know that most hardwood suppliers offer 1/4" thick woods in various species - walnut, maple, mahogany, and even some exotics. And you can get 1/4" oak and poplar at Home Despot.
Sounds like you need to find a woodworker who can cut the material to your specifications.
One minor concern - mounting prints directly to wood is supposedly not archival. (I say "supposedly" because I have a print here in my study that I mounted to a piece of masonite about 25 years ago, and it shows no sign of deterioration - maybe some woods release more chemicals than others, and maybe its just that masonite is a manufactured material.) I would think you could laminate a layer of aluminum foil between the print and the wood that would never be seen and that would protect the print from contamination.