How far are ya shootin'? What is acceptable accuracy to you? Unless you have a physical limitation, if you relax your shoulders, stand with your weight properly distributed, and make sure the only thing you move when steadily pressing the trigger rearward is your trigger finger, you should be able to be on target enough to have an idea of where you're hitting. fire five or six rounds then adjust your sight and go again. If you are that unsteady at handgun ranges, (say 15 yards on in), you need to work on your stance. As my grandpa told me, "don't get yourself in a bind. Be comfortable in your stance."
Using these techniques, I can consistently hit a quarter at 30' with my Phoenix Arms hp 22 (another cheap gun with a 2.5 inch barrel and a lifetime warranty)... unfortunately, that makes shooting my little .22 more expensive... :-[ ^-^
I believe you can do it. A vise on a pistol to sight in seems excessive to me. worst cast rest your hands on a sandbag and work on trigger control. Actually, work on trigger control either way. Get some snap caps and do a lot of dry firing is more good advice.