Tritium is a
beta emitter and does not emit alpha or gamma, and since beta radiation cannot penetrate the glass capsule the tritium is in, such things as Glow Rings and tritium gunsights do not emit any radiation at all (except light).
The rest of this post merely explains that and if you're not interested in nuclear physics you can skip it.
When radioactivity was first discovered nobody knew what the three kinds of radiation emitted by radium were, so they named them alpha, beta, and gamma radiation to keep them straight. Those names are still used even though we know what they are now....
An alpha ray is a helium4 nucleus -- two protons and two neutrons; a beta ray is an electron, and gamma is electromagnetic radiation of higher frequency and shorter wavelength than x-rays.
Tritium is an isotope of hydrogen, hydrogen3, with one proton and two neutrons. It beta decays to helium3 -- one of the neutrons emits an electron and a neutrino, leaving a proton, and we're left with two protons and one neutron. The neutrino goes off harmlessly into space. The electron strikes a material lining the capsule which responds by emitting light.
Although it's moving at high velocity a beta ray is only an electron, a particle of little mass which because of its charge interacts strongly with the electron shell of any atom in its path. A beta ray cannot penetrate a sheet of paper, or the outermost layer of your skin, or the plastic capsule tritium is enclosed in to make a Glow Ring. Thus, although there is radioactive material inside a Glow Ring, it does not emit any radiation as long as the capsule is intact. Even if the capsule breaks it won't do you any harm.
By the way, charge is conserved. You can think of a neutron as a proton and an electron stuck together by magnetic attraction. It takes energy to make them stick together, and when they are divorced by beta decay that energy is released in a neutrino and in the kinetic energy of the electron (its velocity). We're left with a helium3 atom which still has only one electron (since it was only recently a hydrogen atom) so it has a net charge of +1 -- but we're also have an electron speeding off, which has a charge of -1, so electical charge is conserved, and since the electron cannot leave the capsule, the net charge of the capsule remains neutral. The free electrons eventually join up with the helium3 ions to form neutral atoms.
I hope I haven't bored you too much. The point is Glow Rings are perfectly harmless and you can even carry them around in your underwear if you want with no fear of having children with three heads.