Shimmy can be caused by several things, and made worse by combinations of things. Any shimmy is caused by a problem and that problem should be fixed! Condition of tire, air pressure in tire, balance of wheel/tire assembly, loose axle bolt, bad wheel bearings, spoked wheel out of true, wheel bent, loose steering neck, improperly serviced struts, improper air pressure in air shocks, windshield installation. I don't think the windshield by itself will cause a shimmy, but in combination with something else it can contribute.
With the front wheel off the ground check: condition of tire, air pressure, balance (it should stay anywhere you put it - if it turns after you let go get it balanced!), spin the wheel and make it isn't eggshaped or warped (if a spoked wheel is eggshaped or warped get it trued!) (if a non spoked wheel is warped replace it!), grab the bottom of the struts and push fore & aft and side to side (if it wiggles there is a problem in the neck), check that the struts are properly serviced with fluid and if they are air shocks check the air pressure.
My own bike had a shimmy once as a result of a blowout! And I had a customer bring his bike to me complaining about it havimg a shimmy. It was a Royal Star with air shocks; the pressure on one side was 7 the other was 45 with the proper 15 in both sides the problem was cured.
Believe me; having had a blowout with a firm grip with both hands, you don't want it to happen if you arn't hanging on (you may never get hold of the handlebar again)!

Clifford