Are there any distance-learning Chinese (the language) bachelor's programs, or some sort of East Asian Studies degree? I know it might seem like a niche program, but it's something I might be interested in doing. Any and all help is appreciated.
Here is a master's program at Leeds University: Online MA in Asia-Pacific Studies - East Asian Studies, University of Leeds, UK
Anything else, apart from UMUC's program, offered state-side? I feel sort of weary doing a program from a school in another country, or is my fear misplaced?
As long as the schools are legitimate, and both UNE and OUHK most certainly are, then degree acceptance shouldn't be a problem, if that's your concern.
The demand for DL bachelor's degrees in East Asian Studies may be rather limited. UMUC may have the only such program in the US, and College Navigator indicates that they only issued six bachelor's degrees in this field in 2010-2011. That was out of 3,270 bachelor's degrees total.
This is a five-course Certificate in Chinese program from U of Hawaii that can be completed online. However, note that it consists of two 300-level courses and three 400-level courses. In other words, you need two years of introductory Chinese before you can begin taking courses in this certificate program. It's not intended for beginners.