As Kijanki indicated, HDMI is supposed to be hot swappable. However, there appears to be significant anecdotal evidence that can be found on the net suggesting that not all designs are implemented as they should be. The result in some cases being lockups, recovery from which may require power to be cycled, and in some cases even damage.
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?
Yes. But before concluding that any differences you may perceive are attributable to the cables I would suggest that you verify that the same differences are perceived when the connections of the two cables are interchanged.
Regards,
-- Al