No, it will just cover up them up. The cause of the shimmy/shake, will still be there, and will eventually just wear down the new steering stabilizer and you still have the same problem. Tell us more about your shimmy. Does it occur at certain speeds, like around 50-55 MPH? Does it get worse or better if you drive a certain way, or speed, or on certain roads, or weather conditions.
Steering stabilizers are just shocks to absorb lateral blows, they don't fix shimmies, shakes or death wobble. I have 140,000+ miles on my stock stabilizer. I'm sure it is worn out by now and if I took it off and drove around without one I wouldn't notice a difference. If the steering/suspension components are in good shape and properly tuned, then the job of the SS is very minor. Look somewhere else for the problem. Shoot, take the SS off for a little while so it doesn't cover it up to help you track down the culprit. I would start with the condition and balance of your front wheels and tires, especially if the shimmy is around 50-55 MPH.