Hi Ross,
I don’t follow 100% with exactly what you are wanting to do, and I have no idea how your rig is set up but here are some ideas.
-Does the hand need to be constrained to the gun? Can the Gun be constrained to the hand?
-you could add a child-of constraint on the hand (to the gun) which should work fine. Except if there is already parenting on the hand (say to the Root bone) then if the parent moves you will get double transformations. This is a solution but you need to be careful with how you animate the scene. If the parent moves – you can’t use this method.
-Use a “copy transforms” constraint on the hand to the gun. However, because you will probably need it to be offset you won’t want to constrain directly to the gun. Add an empty, put this where you want the hand to be in relation to the gun, parent the empty to the gun, then constrain the hand to the empty.
Hope these solutions work for you.