Ava: It could be that the "wavering" your experienceing is just the natural movement of the scope on target. It's virtually impossible to hole a scoped rifle "dead on" without some movement. Absolutely the best means is to have a good rest for the rifle or a pair of shooting sticks.
The only way to see how that 35 will affect you is to try it. If the stock is a good fit for you and you feel comfartable, then try taking a shot. You never know, you might handle it well. The main thing is to use the rifle your most comfortable with.