I'm guessing these are relatively lightweight, right?
Clear film straps would certainly be strong enough and convenient to use, but if the leather is fragile, the straps' sharp-cut edges may be a problem.
Would a few straps of Stabilitex work? That fine mesh fabric is not very strong, but it is quite supple and would probably do no harm to the mocassins. Because it comes in a variety of colors and is almost transparent, it might be less visible than clear film.
Whatever mounting material you choose, it will probably involve wrapping over a portion of the outside of the mocassins, which would impose some amount of pressure. If possible, I suggest making a shallow sink-mount for each shoe, just to relieve the gravitational stress.
Also, perhaps it would be a good idea to stuff the mocassins with a non-invasive, removable material that would prevent them from being crushed by the mounting provisions. How about carving the shapes out of ArtCare foam center board pieces stacked together? If the stuffers are visible, you could cover them with a fabric matching the interior of the shoes.