How can I move sink supply lines from the floor to the wall?
If you have access to the space below this floor the best course of action would be to re-route these water pipes so that the riser portion comes right up under the center of the thickness of the wall that you show here. Then you would just be opening the drywall here to put elbows on the pipes to bring them out of the wall. 

Opening the wall first from this upper side would be a good thing anyway because it looks like replacement of the wall board that was behing the old cabinet could be a good thing depending what it is that is causing the dark brown and black spots.