Are HDMI cables hot swapable?

No, you have to be careful. A few of my cleints blew up the hdmi switch Please put off everything and then swap.

I would turn off my amp regardless

I accidently blew the video board on an Integra home theatre processor. It was 2 months shy of end of warranty so they covered it (I had to pay s&h both ways) but was very grateful as it would have cost over $500 otherwise. Integra was/is insistent that you unplug both units you are connecting hdmi cables to/from.

OK, seems they are not swappable. So...

I have a new cable that I want to compare to my existing cable. I have an Oppo 105 that has two outputs. So, can I just plug the new cable into the other output on the Oppo (and to a second HDMI on the TV) and then I could just switch between the inputs/outputs via remote control to see differences in the two cables?

Every manufacturer I am aware of tells you to power down everything when making or breaking any connections. I don't have anything using HDMI so I am not certain about it. What does your manual say? Personally, I would never do it hot, the risk seems too great. If it is that hard to turn off everything for you, and you don't mind taking that risk, by all means do it hot. Good luck with warranty if you blow something up doing it hot.