Well, what matters here is what you want to do. Are you OK with going into the race without having run a 10K before? Of course, you do have a month... I'm sure you could ramp up to that distance and run it at least once before the race.
For my Oly I was trained to run the entire distance and I walked a lot of it. The heat beat me down into submission.
And the interesting thing... is that a lot of people were walking the run in the Oly. More so than what I would have seen in a sprint. So, you won't be completely out of place walking.
Good luck!
"Life is not a journey to the grave with the intention of arriving safely in a pretty and well preserved body, but rather, to skid in broadside thoroughly used-up, totally worn out, and loudly proclaiming: WOW WHAT A RIDE!!!!"