You used to be able to kill deer, foxes and badgers with 10mm and a q15 bow and q15 bone arrow by one shotting them if you wait for the bar to go very high. I'm not sure how perception will affect it. This was easily done by aggroing them across rivers or cliffs, and then they just stand there waiting for you to shoot. Also, boars can be done with the same amount, you shoot at them, then deaggro and run away, as they get scared. After that you can just walk up to them and chase with your fists, on jog you outrun them and they won't attack you.
Lynxes can be easily oneshotted with a ~60+ substance arrow and bow, if you can't one shot them you'll have to trap them or leave them as they can't be chased. Moose can be shot from cover at until they run, then use the boar style and run backwards and deaggro, and after that find them and stand on them charging up the bow as they don't aggro by default and run too fast to punch.
Bears are difficult to do without any defensive stats, unless you block them in with an alt in any manner whilst standing behind cover. If you have a high quality bow that can deal over 400 damage, you can shoot them from out of aggro range if it stands still for long enough, then aim another shot as it runs at you and shoot just before it can hit you, 2 hitting it. If the first shot misses however, the bear is very likely to aggro you and take you out.
Alternatively, you can use this
exploitmethod with any mm and q bow/arrow on any animal:

Note that the animal will break the boats/stockpiles/whatever you use if they stand between the aggressor and itself. Animals don't break in flee mode however (this method is still viable despite the screenshot's age). Two boats can block animals on any river, however you will need an alt to place the boats.