Most glues will leave some type of visual stain. The glues that won't leave some type of visual stain probably won't stick as well. For example, you can use rubbery RTV type glues, but you will need surfaces designed to minimize the need for glue strength. However, an advantage is the glue will flex.
My favorite is Gorilla impact resistant superglue. Superglue breaks easily when flexed if not impact resistant. If you want to go to the trouble, epoxies are best. Rubbery type glues will work if you have enough surface area, especially if it is not all planar.