Soldering on the end.
Once you cut the barrels, which are soldered together, you will have a small hole between the two at the new muzzle. If you do not seal the hole, water and "stuff" can get in. Also, the soldering would return a tiny bit of strength lost from cutting the original joint. If you are not particularly concerned about appearance, JB Weld would probably work as well.
Despite the romance of shooting a shotgun from the hip - and maybe there are some folk who can do it well - it is a remarkably inaccurate way to shoot. Over the years, I have had the dubious pleasure of watching shooters shoot pistol grip shotguns and "cut down" guns from the hip. I cannot recall any of them hitting the target at which they were shooting. A number of them, I remember clearly, missed the berm behind the target. Your mileage may vary.