I would absolutely not hesitate to use contact cement to repair loose veneer. To do it right you must apply it to BOTH surfaces and let it flash off. (let it sit until it becomes clear) Once it has flashed off the stuff will bond to itself like you wouldn't believe. A thin even application is all you need. A good idea is to cover any veneer in close proximity with painters tape in case it gets slopped around.
Good luck
Good luck