Well, virtually every Okinawan weapon has a Chinese counterpart. The only exceptions I can think of are the Eku (oar) and Tonfa, and this is probably more indicative of my lack of CMA knowledge than anything else. Nunchaku/sectional staves existed in China, and looking at pics of old Okinawan weapons, it looks like old nunchaka were actually weighted flails instead of being symmetrical. See: http://museum.hikari.us/weapons/index.html.
Patrick McCarthy's theory is that karate developed among the minor aristocracy: folks responsible for law enforcement. In the feudal era very few people were responsible for defense and policing full time, so it's plausible that martial artists would develop drills based on the everyday tools they had on hand. Looking at vids of Fujian White Crane forms, I'd have to say it looks an awful lot like some karate kata.
Okinawans did have an indigenous wrestling form that's sometimes called tegumi, though now it's awfully confused, given that tegumi is now a term for some kata bunkai and the wrestling form itself is now called "okinawan sumo," despite the fact that it doesn't resemble Japanese sumo in the slightest (contestants wear jackets, there's no Shinto component or dohyo, and victory is determined by shoulder contact).
Seikichi Uehara also claims to be the inheritor of an art called Mutubu-ryu Undunti, which he says is unrelated to karate (though it is now apparently taught along with Shian Toma' Seidokan). Reading an old JAMA article, it seems to resemble jujutsu more than karate, but with an array of Okinawan and Chinese weapons (including the sabre). Uehara is (or was; he must be at least 100 by now) an acknowledged Jo-odori (short staff dancing) performer).