I suppose it's possible to smuggle fertile cats in, but it's really far-fetched. According to another comment here, this remote island has a single ferry. A howling cat in a carrier is going to be easily noticed while boarding the ferry or traveling on it.
I said try not succeed, though it wouldn't be that hard to sedate a cat for thirty minutes or find a boat.
I think some people will think this is a travesty they can fix. Even this thread has some amount of people who don't seem to realize this is intentional and the alternatives aren't great.