The approach would depend, I'd think, on the video quality vs bandwidth/real-time requirements
GoPro has an article on GoPro as a webcam (presumes USB connection to a computer)
I'm presuming, a small computer isn't realistic, right? IN which case, doing a HDMI capture also probably isn't viable (unless for in-car, where power and weight less of a concern)?
You could go the cellphone WiFi connected to the GoPro to get the video?
All o fwhich points to it being a real hassle. with the cost involved, and presuming GoPros themselves aren't the issue (ie a GoPro marketing video), I'd be inclined to consider an alternate device with native cellular connectivity