You can make a trap of sorts for the Cubans, Melanie. The UF site tells how to do it - just get about a 2ft. piece of 2in. PVC (plastic pipe). Cut it at an angle at one end so you can easily stick it in the ground, then just leave it there and the Cubans will hide inside there in the daytime because it's cool and shady. I have 5 or 6 of them around the yard, and I can trap a Cuban just by putting a ziploc bag over the end of a pipe with an elastic band, and sticking or spraying something in the other end. (I use Benadryl antihistamine spray, it also puts them to sleep in about a minute so if they do escape they are very slow) They hop out into the bag, and then you can just put the bag into your freezer to euthanize them. No whacking involved.
I usually hide them away in the foliage so they don't show up but I moved this one so I could get a picture of it.