Live-stream HD camera to stream on one's own Wordpress website
I think the answer to your question depends largely on your budget. A pretty easy and standard config (but which is not really cheap) would be using GoPros with the corresponding helmet / head mount and plugging it into something like a Teradek VidiU http://teradek.com/pages/vidiu - configuring it for your favourite streaming provider and pointing your WordPress plug-in to show that stream.

A wired article about the vidiu and two other streaming devices:
http://www.wired.com/2014/10/hd-streamer-boxes/

Depending on how long this needs to run, you should maybe add an additional battery solution to the setup, the vidius internal battery only seems to run for 60 minutes...

Apparently GoPro themself announced a streaming transmitter / receiver System called heroCast but it seems to be even more expensive than the teradek.

Alternatively you could use a smartphone to do the recording / transmitting with something like the bambuser app / service, most certainly the quality will be worse than the GoPro / vidiu solution, but cheaper. For both solutions you additionally need to make sure you got a decent WiFi coverage for the areas you want to be part of your project or - broadcast the stuff over LTE / UMTS, involving extra cost for the appropriate data plan you need to get in that case.