You probably won't catch anything dangerous on a Kastmaster. I only relate about actually catching sting rays because of my method of fishing. I would fish with bait (small pieces of squid) until I caught a corvina, then switch to Kastmasters or other lures. Why? It can get pretty boring cast after cast catching nothing. Plus, I used to always have the kids along. They want to catch something, anything, and none of them could cast a lure without taking out somebody's eye - usually mine! So, I'd bait fish to keep them occupied until the corvina came through, then it was Dad's turn to have at it and they could hit the beach.
Some of the usual suspects you can catch at La Pinta on bait are small triggers, the ever-present sand bass and sting rays, mojarra (porgy), small pargo, wrasse, and some other little assorted odds and ends. That is, if you cast out into the deeper part of the channel at low tide, or as I used to do at times, use a 12 ft. East Coast style surf rod that could fling a 4 oz. pyramid sinker all the way across Baja to the Pacific! I also used to wade fish the sand flats from La Pinta down to the back bay at the end of the beach at San Jorge, fishing Texas style - a small lead head jig with a rubber Cocahoe minnow. You can nearly walk out to the island at low tide. The sand flats, however, are a wasteland and after a few times of trudging around out there in the heat without even a bump, so much for trying that again. The corvina, like Texas sea trout (specks), like to run in the deeper cuts, exactly like the channel that forms La Pinta. As Ed B mentioned, I've also caught them in the harbor. They often move in and out with the tide.
The only thing I've ever caught at La Pinta using lures are corvina and pompano. Once or twice, I managed to snag a mullet. Off the rocks near Cholla, I've caught needlefish in the summer months. You'll know them - they are long, skinny and silver like a barracuda, but have a much longer snout that's full of teeth. In Baja, they grow to be giants nearly 4 ft. long and will attack any shiny lure, but they all seem to be smaller models off of Cholla. Sierra and barracuda are also possible near Cholla, as well as some big orange mouth corvina. Ric has pulled in some hefty ones there.