What do you mean by "shimmy"? If you mean it shakes its head on rough surfaces, that is something I do not worry about.
Over the years I have had 3 Ken Rogers, 3 Longstaffs, 1 Chris Paulson, 1 Higgins, 1 Trykit and a couple of conversions. My 1972 Rogers (built for me) was a bit sensitive to tyres. It was fine on tubs, but on pressures a oscillation could be induced. Back in those days we called it "speed wobble", or at least we tricyclists did. My Trykit is a bit sensitive to a barbag when on tour, but that is all.