What percentage of NPC missions are non-combat?

The latest patch has changed this significantly. There are now only three divisions:
Security - All combat missions.
Distribution - All courier missions.
Astrogeology - All mining missions.

It depends on which NPCs you talk to. Some NPCs ("Command" NPCs) mostly give combat missions, some give mostly mining missions.

http://wiki.eveonline.com/wiki/Missions_Guide

That page has a table (Corporation Division vs. Mission Types) which contains the probabilities of each mission type based on NPC type.

If you don't want any combat missions, try "R&D" NPCs, they have 0% combat missions.