How will liquid nitrogen affect a steel instrument's ability to function?
Metals become brittle as low temperature (and that's why you cool your Parr bomb in a dry ice bath, never in liquid nitrogen when you condense gases in).  But the worst thing that can happen is that a claw might break off, which shouldn't cause any damage to equipment.  Why not try in a small dewar first.  Liquid nitrogen is cheap.

A good alternative to racks of storage boxes are storage canes, such as these.