I think you are going to have a rough time finishing the veneer by hand and especially using a wipe on varnish. Most anything you wet the veneer with is going to make the veneer wrinkle. I think if I were going to do this I would use lacquer and spray it on and in very thin coats. I think lacqer would dry before it affected the veneer so much. It would also be better if you would finish both sides. If you seal one side the humidity in the air will affect the veneer. If you don't have the means of spraying, lacquer can be purchased in rattle cans.