Several frame designs can be opened & reclosed: Nielsen's 100 series has 1-11/16" useful depth, which might be enough for a pistol, and an be fitted with rail hinges to open one side like a boxtop; Framica Boxers have extenders for any depth, which can be hinged or magnetically latched; an acrylic box can be used with a wood or metal base-frame fitted for opening (Gravity Groove is my favorite). Several designs will be detailed in the all-day class, "Complete Guide to Shadowboxes" in Las Vegas later this month.
To mount the gun I suggest using several steel or brass rods, bent to fit the contours of the gun at convenient mounting points.
10mm Polyflute makes an ideal mount board (non-hygroscopic, dimensionally stable, chemically stable, rigid, lightweight, cheap), which can be covered with any material you like. Cut a hole in the back skin of the polyflute and fill the cavity around the rod, between flutes, with hotmelt glue.
Cover the exposed part of the rods with shrink tubing to provide a pad and an inconspicuous matte black (or other color) mount.
Acrylic sheet or rod can be heat-formed, as well. Likewise, wooden pegs can be shaped to fit, and covered with suitable material.
Hope that helps. If these suggestions aren't clear, you're welcome to email me privately.