Well you definitely wouldn't like Perilous Hearts then!
Try Rode to Rage or Technoshock with Locudus's sound mod (only animal is a robotic mosquito) for shooters, and run for your life, oh shit, Kringle Crash, Bloodshed Release the Pain, Scrolling Battles 9.6, The shooter concept demo, Crime Hunter, 2D Platformer, Deathmatch Project Alpha, or The Blood Rain for side scrollers.
Also try legacy as an adventure game, and maybe Sarah and the Castle of witchcraft and wizardry as well if you are comfortable with killing a giant magical snake monster (not graphic or actually required to beat the game) or making a cat sleep with a stunning spell.
Those are all the games I can think of that I'm sure don't have animal killing in them, that fit your genres. You can grab most of those right from audiogames.net by looking under the games link or using the combo box on the front page, but you'll have to get The Blood Rain direct from ch-games.ru/en and Legacy from Right here
You can get the Technoshock mod from this link and you can get Shooter, Crime Hunter, 2D Platformer, and Scrolling Battles 9.6 (which is in the old games archive) from the "masonasons.me" website.