I have taken my zapper in my carry on bag on several airplanes. I have not had any problems going through security. I once had my laptop and a scanner radio and a small portable ozone generator the size of a pack of cards and my electric razor and they all had their batteries installed. I had to open my bag only once because I had two small glass bottles of tinctures in the same bag. I was asked what they were for and I said they were cold medicines. The security person said okay and let me pass and never questioned the other stuff in the bag.
If you are unsure, you can put the zapper in a checked bag, not your carry on. Or keep the zapper in your carry on bag and the battery and the hand holds in the checked luggage.
I have no idea what problems if any you would expect in Central America.
You could carry a copy of Dr. Clarks book with you. That way if you are questioned you could show them the part in the book about zappers. Plus you will have a good book to read while on the flight.