No, wrap 20 or 30lb spyder wire around the outside. Cover it with electrician's tape. You can get a good 50' around a K&M. Spyder wire is strong enough for light shelter building, snares, sewing and as a trigger for traps.

In terms of content's (and yes I have already done this ) I suggest the following:

2 x sail makers needle's.
4 or 5 strike anywhere matches.
4 Tinder-quick (on a string).
4 hooks.
Split shot.
X-acto blade or similar.

Forget about water purification. That should be with your water bottle / bladder.

If you have any space left - add more matches. But don't overfill the case. You are only planning for a weeks worth of fire lighting at most.