Given my flair, I should probably quickly answer for early 19th century New Zealand. The answer is mostly no: the pre-contact Māori were pretty unbothered by by 'creepy-crawlies', most people had lice, and would actually eat them when they caught them. A couple of small creatures: rats and huhu grubs were actually food sources. The only exceptions to this (a near universal fear of lizards for instance) were rooted in superstition, and therefore rational. Small birds such as the fantail were considered omens of death, and lizards were associated with disease, death and evil: many diseases were understood to be caused by a demon in the form of a lizard eating you from the inside (it's possible that the origin of these beliefs may have been an irrational dislike of the way lizards move or something, but as experienced by a 19th century Māori person, it was understood to be a rational fear).

Anyway, the first thing I thought of when I read your examples was the always entertaining Usamah ibn Munqidh. A twelfth-century Syrian nobleman, Usamah wrote a book about the importance of fate that's essentially a collection of weird stories. Here he talks about brave men that were afraid of small animals (Such was the spirit of daring in this man... and yet if he should see in his house a snake, he would go out in flight, saying to his wife, "It is thy business to kill the snake!"). A couple of pages later he has a few stories of people that fainted at the sight of blood.