Tamid I have done this type of Shim The Hook repair for many years, after many methods tried over the years I found that the best method of fixing the shim for me is Solder but not just any solder.
Firstly, if I shim a gun to improve matters for another person rather than for myself I always use a brass shim stock, so it can easily be spotted if the gun where to change hands.
For my own use I use steel shim stock.
The solder I prefer for this work is electrical/electronic grade 60% Tin 40% Lead SOLDER PASTE it is easy to use and makes no mess at all by running out of the joint.
Clean the hook and the shaped shim I use 1000 grade wet and dry abrasive paper then degrease, apply the solder paste to the barrel hook (the solder paste is a mixture of fine particles of solder in a resin flux paste) then fit shim. Keep the shim in place using fine wire, clean any paste you may have spread to other parts then heat the area gently. Now the melting point of the paste is normally no higher than 140 degrees and just to make sure I leave a very small amount of paste close to the shim so I can see when the solder in the paste starts to flow then stop heating, though always heat the hook metal so the heat travels to the shim not the other way around.
