If I am not mistaken, I believe the Polynesian's paths connect to the GF and it's about 1 mile. It's very safe. When you check in, ask for a resort map and ask the CM to point out the jogging trail. You could also check out Tikiman's website.
Edited to say: tried to post a link but could not. Sorry!
There is a ton of detailed info on this site. Hope this is helpful for you!