Rich, I wasn't trying to tell you what was causing your shimmy, just sharing my experience that may be causing it issues as well. Your symptoms can be caused by anything from poor wheel balance, tire cupping, rust on the hub causing the wheel to be mounted off-center (always sand it down and apply anti-seize), or any worn suspension component. I wouldn't put the shocks on the top of my list, but after 200k, you may be better of counting parts you can keep rather than parts to replace.
Have you tried wiggling a wheel and tire up/down and side to side? If there is freeplay, you should be able to pin point the (or a) culprit. Mine was the front ball joint on the driver's side, which requires a new control arm basically (pair). If you don't have any noticeable freeplay, it may be time to do a deeper inspection of the front bushings and joints using a pry bar.
Oh, and if you are able to detect the shimmy in the steering wheel, I recommend concentrating on the front;conversely, shimmy felt through the car seats and floor are more likely indicative of rear end vibration. Good luck and post back if you are able to narrow it down!
540i - Stock/Sport / 6MT / 13.9@100mph
WS6 - 231/234 / 6MT / 4.10 / 410rwhp
ITR - 262/262 / 5MT / 12.2:1 / 9600rpm
540i/6 Sport, Jet Black, Style 65, LED tail, DICE+GROM USB, !CDV, Redline MT-90, M1 0-40w