I hardly think so.
Flappers in the 1920s did it, in Britain and Canada anyone wanting to climb a flagpole will do it (though why anyone should wish to climb a flagpole...), Russian gypsies do it; and so do bellydancers, badly maintained vehicles, and of course the inimitable Jeeves.
The 1920s dance was a vigorous shaking sort of thing (one of the first shimmiers, Gilda Gray, claimed to be shaking her chemise, geddit?), and the idea of the similar gypsy dance was to rattle the ornaments on the dancers' clothes. (Russian Gypsies called this shimmying dance a tsyganochka.)
A shimmying car is also shaking, probably because its front wheels or steering are faulty. That sort of shimmy is also known, worryingly, as a death wobble.
But shimmying needn't be energetic or undignified. The most dignified man on earth, Bertie Wooster's gentleman Jeeves, quite often shimmies into a room. In this case to shimmy seems to mean to appear silently, as if by magic.
If you manage to make people utter a squawk of terror when they discover you at their elbow then you'll know you'll have got it just about right.
On the other hand, if you fancy something a little more active:
Thing To Do Today: shimmy. The word meaning a shaking dance may come from chemise, which means blouse and has sometimes mistakenly been thought to be a plural. Mae West claimed to have invented this dance, but probably didn't. There was a 1917 song called Shim-Me-Sha-Wabble by Spencer Williams which may have been the source of the name, too.