I have pinned down the technique on how to make a shadow box frame, but what is still elusive to me is how to mount the print other than dry mounting.
It seems to me that in any way you do it you must apply adhesive to the image which really isn't a good archival practice and at the same time involves some risk that the print might fall over time.
Any idea?
Technically, dry mounting, although permanent and secure, is not archival. The reason archival conservative framing methods are completely reversible is so that the mounting board and mat board can be replaced over time as they get contaminated. This is usually an issue for museums and less of a concern for most photographs especially those that be reprinted. You can also use archival t-hinging which is fairly easy and inexpensive. This method often relies on the matboard to help keep the image flat but in the case of a shadow box having some curve to the print may add depth and texture to the presentation. You can click here for overview on mounting techniques.
Some drymount tissues are reversible, but would still only consider that coservation not archival. T-hinge mounting would work but over time will let the print sag and eventually dislog. This should take many years if the right technique and materials are used. May also want to try a pass through mount as i have found them to be stronger.