Yes, tritium is radioactive but it has to be recycled and reused to continuously fuel the reactor. Every part of a fusion reactor is designed to minimise the retention of tritium, the actual radioactive waste will be materials activated by neutron radiation (neutrons are captured by nuclei, transmute the element into a radioactive one which then decays to a stable isotope emitting more radiation).

A small fusion reactor, being a powerful neutron source, will be a great risk for proliferation. It should be able to breed plutonium for nuclear weapons as much as it can breed tritium.