No matter what animal, I always wash ! This way no cross contamination and, it's just hygienic. I also keep some hand sanitizer by each enclosure and labeled which dragon, or reptile it goes with.
Janie.
They say you should wash your hands after handling you lizard, each time. They carry salmonella, so you really want to make sure you wash good before handling your food.
You should be able to use hand sanitizer. But I think you'll find if you use that a lot each day you may get very dry hands. It's full of alcohol. You might be better off using a antibacterial hand soap if your concerned about the salmonella.
It won't kill you, but it can make you really sick. I got salmonella from Jasper once, and it was totally my fault. I was holding him, petting him and eating popcorn with the same hand. I picked up salmonella and was really sick for about a week. Trust me, this is not something you want to experience. Extremely painful abdominal cramping, constant vomiting... it's a lot easier to just wash your hands.