I can't speak of the trigger tuning, but the stock can definitely be cut and a recoil pad ground to fit the 96/44. I hated the original curvature of the stock butt as it seemed to drive the toe of the stock into a nerve in my shoulder. I ended up raising the comb of the stock for a better cheek weld in addition to cutting the butt flat and installing a grind-to-fit recoil pad. Between taking out the sharp toe and adding a cushy recoil pad, the rifle handles completely different-- more like a 77/44 than the 96/44 (much more shooter friendly, in my book.) I left the LOP the same as the original stock, but I took about 3/4 inch off the stock to accommodate for the recoil pad. My stock was beech-- which is notoriously tough to stain or dye, so if you like your current finish, tape well and cut very carefully with a fine tooth saw and maybe even score the surface with a knife, first.
hotmail.com) and ask him if he works on 96/44 triggers. I know he used to work on 96/22 triggers and has a good rep on Rimfire Central.