Shake a leg

I agree, whatever the origin or the context, "shake a leg" means to "get a move on", "hurry it up", whether it's to get out of bed or to get something else done.

Your origin on this refers to showing a leg to prove your awake. That may be so, but I doubt it has any connection with "shake a leg". I think a more reasonable explanation of this would be to run. We do sort of shake our legs when we run. In the US, it means to hurry, or make it snappy.
ES