They are not infected! They just passed quarantine!
As for the riding, if the whale agreed to the concept, maybe a harness of some type could work? It would however cause major drag… so perhaps a streamlined compartment or, well, pod, for the human would be better. Built of the same self-adhesive material the cat rank collars are?
Which reminds me, some old art by Minna has very cool steed concepts featuring fantasy animals!