“Katte-” as a prefix means relating to a cat. Eg. “Kattepoter” = “cats paws”
Gat means the cloaca on a fish or a bird (cloaca is the all-in-one hole on fish, birds, etc.)
I realize this is probably a very wrong interpretation, but in that case, i don’t want to be right.
You’re close, the name does derive from kat and gat, dutch words for cat and gate/passage/hole, respectively. The safe routes were so narrow, even a cat would have trouble squeezing through.