My base art was called Ryukai Kenpo and was very light on kata. The history I was told was that it was a fusion between Te and Shaolin martial arts.
I was not introduced to full kata until I had spent 5 years in the system. Learning the first kata was part of finishing the Seigansha (petitioning student) stage of training.
Subsequent research on my part has led me to believe that it is a hybrid of Kojo-ryu (or something similar, since a few of the animal styles referenced in training are not used in any other Okinawan art) and jujutsu. My teacher's teach was Japanese and not Okinawan, so this seems plausible.
After quite a bit of reading I think that Okinawa had at least two unarmed and one armed martial arts with little or no kata: Te, Tegumi and Okinawan weapon techniques. Very few threads of these arts remain; modern Tegumi is now called "Okinawan sumo" despite the fact that it isn't much like Japanese sumo. Tegumi matches were central to my own training. Patrick McCarthy believes that early Thai and Indochinese arts may have informed te training, and demonstrations of krabi krabong and muay boran do look somewhat technically familiar to me.
In my personal view, form-oriented Chinese martial arts really took root some time in the 18th century and were combined with te in a haphazard fashion. It looks like early to-te masters cherry-picked kata that fit their te-informed fighting methodologies. It also looks like the central point of karate transmission through the Meiji period was through people with close ties to the Japanese administration, while te was left to wither on the vine. Nowadays, I'd say that pure te died with Seikichi Uehara. This is a pity, because the te/tegumi elements I've seen in my own training, in articles and elsewhere are radically different from contemporary karate: far more relaxed, little emphasis on kata and in terms of custom, somewhat more informal.