The Whiteman builders, particularly Dr. Bob there, says that much of the shimmy in wheels and nose wheel is due to lack of balance in the wheel - a little balancer is available at Go Kart shops and the lead weights are easy to apply in the rim. I'd never heard much of this - but he says smooth rollouts are the very quick and obvious results. As for the main gear, he balances those wheels too, but he also uses the center point of the axle to add weight to the nose of the wheel pant and balances that too - so that it is not tail heavy and driving motion on the gear.
We had a guy with such shimmy that he was shearing the bolt that held the outside of the wheel pant on, on every landing.
