Veneer is pretty easy to use. I am veneering some cabinets in my master head. Doors were originally just white. Lots of instructional videos on YouTube. Straight-edge, ruler, razer knife, scissors. Not much required. I am an amateur woodworker but this is far from the most difficult thing I've attempted.
I ordered real wood quarter sawn teak veneer on line with a 3M Pressure Sensitive Adhesive backing so no glue. Came in a 2x8 sheet. Stuff holds like the dickens. It would be simple to veneer a sheet of plywood to fit your needs and likely cheaper than buying a full 4x8 sheet of teak veneer plywood that you may never use all of.