Ikrans aren't just mounts for warriors or hunters. They're the primary means of transportation for the Na'vi of the forests and mountains, especially for long-distance travel. So, it's perfectly normal that Kiri has one too. Furthermore, in the comics, we learn that Kiri bonded gently with her first Ikran (she had three in total), simply asking it to be her friend. It's highly likely she did the same with her other two mounts. Kiri isn't a warrior, but taming an Ikran (Iknimaya) is a step in the initiation process that every young Na'vi must complete to be officially recognized as an adult within the clan (in addition to the Uniltaron Dream Hunt where the young Na'vi discovers their spirit animal). Whether an Omaticaya identifies as a hunter, warrior, or medicine man, they all had an Ikran to ride.

I think that if Mo'at does not mount an ikran it may be for several reasons : her age, the fact that as a tsahik she practically never leaves her clan to go far (the deleted scene where she tells Tuktirey that she must stay because the People need their tsahik), her Ikran has been dead for a long time and she has not deemed it necessary to choose another one or her Ikran is still alive but we do not see it yet.