Doubt is not a pleasant condition, but certainty is absurd.
Read or Die
One Week Friends
Encouragement of Climb
Castle Town Dandelion
Girls Und Panzer
Avengers Disk Wars
Most of the anime listed should be safe as far as fan service goes. While most have female leads none that I can think of have "damsels in distress". Any of the girls/women who find themselves in trouble find their ways out of it either themselves or teaming up with others. While a few of the titles may have "cartoon violence" (Avengers/Girls Und Panzer/Read or Die/Tweeny Witches) none of it has blood or injuries.
Favorite anime list at http://www.anime-planet.com/users/Reddawnrocker/anime/...