Don't forget that it's possible that the ice cream scoop wound isn't what actually killed her; it wasn't large or deep enough for that.

Another possibility is that Koishi was disoriented and on the run following the wound to the head, fell into the pool, and was unable to get herself out thanks to having a concussion.

I don't think any of us that remain are strong enough to do someone in with a single blow to the head with an ice cream scoop, of all things.