Wimpish means cowardly

"трусливое отвращение" - встречается, но мне не очень нравится
Как насчет "патологическое отвращение"?

Let’s say you’ve always had a fear of snakes. You take your kids to the zoo and there’s a snake pavilion that you can walk through and it’s dark and humid. Your kids want to see it, so you go through. You don’t quite enjoy it and secretly cringe at the sight of each specimen, but your kids are enjoying it and learning about wildlife, so you grin and bear it. However, let’s say you have an actual phobia - your kids beg to go into the snake pavilion and you adamantly and categorically refuse, offering to sit on a bench and wait for them to come out and even raise your voice and start sweating when they insist, then this might be viewed as a wimpish aversion because you “wimp out” and refuse to go along.