Obviously Walrein for surfing/diving, and Aurorus for just... walking, I guess?
I definitely want to investigate on this, since I love the idea of Ride Pokemon and want to know if some of my favorite Pokemon are rideable.
Please give a source for each Pokemon along with you answer.
As you can see from Bulbapedia's page on ride Pokemon, no, you cannot ride on either of them, in terms of actual ride Pokemon in Sun, Moon, Ultra Sun, and Ultra Moon. Also, as sumwun mentioned, Walrein can learn Surf, Waterfall, and Dive.