The monk was originally going to use the Ki power source, but WotC decided that it didn't make sense to have a power source devoted to a single culture. From the D&D Insider article: "We also didn't want to simply shove all the classes inspired by Asian cultures into one power source for the sake of bundling them together." Psionics -- mental energy drawn from within -- seemed like a good fit.
The rest of the psionic classes could be fit into Ki, but it wouldn't be effortless -- you'd need to do some reflavoring. The ardent, for example, is flavored as an empath, which doesn't drop seamlessly into a wushu-inspired world. The psion is explicitly either telepathy based, telekinesis based, or telecreativity based.
Answering the specific psion question: for a telepathic psion, it could be that the character is so in tune with the social intricacies of the world that she's practically capable of telepathy. Her attacks might be words of bitter scorn, a la the bard. For a telekinetic psion, I'd use those little darts so popular in Hong Kong historical movies. She's not throwing raw force around, she's tossing tiny darts at things, with the proper amount of precision to affect their movement or to force them to dodge. These are a bit of a stretch, but might work for her.