Keep the dog on a leash and let her sniff the cactus when she's calm - if she's even interested. Cactus isn't a very exciting thing for most dogs. The critters that might hang around the cactus are.
I have a "camping ID tag" for each of my dogs. I put them on when we're out in the RV. They have the RV's plate number. Doesn't help to have a phone number in areas with no service or for your home when you're not there.
For first aid kit, my people kit works for most things. I do have the "tick tweezers" that lock closed. Makes it much easier to grab and pull.