Tritium is, in fact, completely safe unless you release the tiny amount of tritium from the carefully sealed and sturdy vial and then inhale it, eat it, or get it in a cut or other part of you not properly protected by intact skin.
It is true that it is much safer than radium, the two are not even in the same category. The most common isotope of radium is an alpha emitter and puts out gamma radiation.
"Tritium is a very low energy beta emitter and even large amounts of this isotope pose no external dose hazard to persons exposed. The beta radiation cannot penetrate the outer protective dead layer of the skin of the body. The major concern for individuals working with this isotope is the possibility of an internal exposure. Such an exposure may occur if an individual contaminates bare skin, accidentally ingests the material, or breathes it in the form of a gas or vapor."