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!