This is the part that is touching the SATA cable / HDD power cable.
I have a very small case, so there is quite a cramped fit in here in regards to the cables. No other cables are tocuing anything, but I'm wondering if possibly the vibrations from the harddrive could damage the GPU since the fin is touching the cable?
more than likely no. I'd be concerned it "melts" the cable. I'm sure it wont actually melt it as such but over time the exposure to that heat could make the cable degrade in quality. if theres is so way at all to run it a different way I'd try. otherwise just keep an eye on it, see if the cable seems weaker when you move it etc.