I have my spare, POS oar that slides underneath the rower's seat and takes up a lot of otherwise useable room. I wouldnt secure the oar with anything that cannot be removed in under a couple seconds. I broke an oar a couple months ago on a 90 degree bend with big rocks on the inside, fast water...just all in all a bad situation (the oar that came with the boat was rotten), luckily I was able to immediately grab the spare oar and get us away from the far bank...had it been secured, no telling what would have happened.
Wherever you find a place for it, make sure it is readily accessible.