Hi
Do you intend to do it on your own? Because that's not going to be easy and will probably involve disassembly of substantial part of the camera. I'd suggest looking for "service manual" or "repair manual" first of all. I have never had Canon, but what you described is "shutter curtain desynchronization" and every single Olympus OM-2S suffered from that problem. Since it is an electronic camera, I couldn't do much.
As for Canon, first rule out shutter squeal/squeak. It may indeed be caused by lubrication problem.
One more thing: I would take one picture of the same scene at all shutter speeds, to see if the problem is on all of them, or only on some. Because on OM-2S it was on three speeds only.