Take a look at the Galloway Run-Walk program.
The harsh reality is that in a week, if you can only run 4k continuously right now, you will not be able to run 10k in a week. Your best bet if you really want to do it, is some sort of the above, where you run 1k, walk .5k, etc. Get used to the idea that you WILL be walking if you go ahead and do the 10k.
If you try to run the entire thing, you WILL cramp, you will most likely be miserable, and end up walking a large portion anyway (If you manage to finish).
Be smart, and you can finish the 10k in relative comfort. Then you can start working on building up endurance for future events.