Judooooo Chop!
Judo actually does have hand chops, as well as punches, and kicks. The real Kodokan Judo regimine includes a kicking form. The highest kick is to the waste, and while the kicks of Judo are intended to be practiced as a way to increase leg sweeping power, they are perfectly valid low kicks. One of the kicks does not exist in any gong fu I have seen, including longfist which my style has 26 kicks.
The kick is lift the right leg, and kick out 45 degrees away from the body to the right, pointing the top of the foot at the side of a knee. Def strange.
The swinging chop from the ear, and a chop to the outside of the body at shoulder height are some examples of the chop in Judo.
Both chopping, and kicking are important combative aspects of the art, since there are some situations, where it makes sense to hit the opponent somehow and not be grabbed.
Shuaio Jiao can be drawn from any CMA as far as I know, and while some schools really like to play with wrestling concepts, some schools don't. I have always been told that Judo was taken from Jiu-jitsu, which was borrowed from Chinese fighting methods. Usually, after someone tells me this, they tell me to show them a throw, and are immediately able to counter it in some creative way that I couldn't have forseen.
I saw Jackie Chan pull off a circle throw in a movie once, with more grace then most judo players.
"Siezing oppurtunities causes them to multiply" Sun Tze