Tritium decays by beta-decay (an electron). The electron can not travel very far in air (1/4 inch), and is stopped by even the thinnest piece of metal. It's even stopped by the dead outer layer of your skin.
Not quite: beta decay will penetrate the skin enough to damage living tissue - beta burns are what caused the fatalities of the Chernobyl first responder fire fighters.
They spent a few hours covered in dust on their coats, and did a bunch of subsurface skin damage which manifested as third degree burns. Sepsis, not radiation poisoning, generally killed them.
i.e. it's completely harmless unless you eat it.