Preemptive zombie massacre, good idea?

Solution 1:

I don't think it is possible or feasible to do so from the beginning, or at all until you get plumbing up.

You need to find the weapons in the first place! Punching zombies costs AP and only has a slim chance of success.
Without a watch tower you have no other way of finding out about zombies other than bumping into them, AFAIK.
Non-water-based weapons break easily and are expensive to repair; water weapons are just too costly before plumbing, not to forget water balloons are strictly throwaway!