Since no has answered this post in the last three weeks I will take a stab at it. The method shown in the video will work and has been used for many years to tighten up loose areas on a gun. As shown in the video in this case it leaves no evidence until the gun is taken apart. Making and installing shims would be very time consuming and require re-blueing. The solder seams may show. If I was not experienced with this type of work I would not attempt it myself. A loose forend it just that loose. Metal is missing and has to replaced one way or another to tighten it.

Also remember to keep the forend screws tight on a 21 as Winchester did not have an adequate system to control the recoil effect of the wood to metal. When shot you hold onto the forend and the gun recoils to the rear causing the the wood to pulled forwards. Over time this will damage the wood. I have seen more then one Model 21s especially beaver-tail models with split wood and bent screws from being shot loose. Later guns had a screw and recoil lug installed in front of the forend iron.