A tip could be practicing a one-legged shimmy.
Stand upright, keep your weight on the right foot. Shimmy on the right side (in my case, thigh/knee-driven). Then shift weight to the left and continue shimmying on the right. And vice versa, of course.
Then do it on both flat foot and in relevée.
After a while, you may try to make the shimmy without the toes touching the ground (handy to know if you are forced to dance while lying on the floor or sitting on the edge of a raised stage ).
So when walking, you could shimmy on both, or just on one side.
(ok, how many of you just got up of the chair/sofa to test it now? )