Is it possible to see the microbes on your hand without using UV light or a microscope?
Given your constraints, the only solution available would require some amount of preparation. If you are so inclined, you can purchase sterile, ready-to-use agar plates online, which you can then inoculate with microorganisms from your hands by simply touching the agar surface with your palms, and letting the plates incubate at room temperature. A day or two's time should be sufficient for plenty of microorganisms to grow, allowing you to demonstrate that your hands have "germs" (although some of the microorganisms you'll find on your agar plate may very well be airborne contaminants if you don't take some precautions).