From an article about a fatal fall in a state park:

He tried to shimmy down to lower ledge and seemed to have lost his balance and fell, said Sgt. Ken Turner, spokesman for the Maryland Natural Resources police.

To shimmy is to shake. A car shimmies when the front wheels wobble. Or, if you would like something more vivid to lock meaning in memory, shimmying is what Blaze Starr used to do so memorably at the Two O’Clock Club on The Block in Baltimore. (Her movements so captured the imagination of the governor of Louisiana, Earl Long, Huey’s brother, that he embarked on an extended affair with her.) The word derives from chemise, which may or may not suggest an original context to you.

To shinny is to climb, specifically by gripping with hands and legs while climbing a rope or pole. It derives from shin — you know, the leg.

If you can distinguish between a gym class and a strip club, you can probably master the distinction between the two words.