The fact is, if you are noticeably shaky at 100mm ... you are really going to hate 200mm. LOL
Best advice on how I counteract "handheld" shake is to practice tightening your elbows against you sides ... take a breath ... let half out ... ease down on the shutter release and ... commence fire.
Often, using "continuous shot" (aka taking two images at a time) can also produce at least one good image, because the initial shutter release press
maybe bad ... but, there is no "second press" to buffet the camera.
(Hey ... if you have a mule ... ride 'em. We're not developing these.)
Just a couple ideas on how to fight ... handshake!