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.
Which is why in "fusion" bombs the majority of energy still comes from fission. The fusion reaction is a neutron source to boost the efficiency of the fission reaction. A pure fusion bomb, if one could ever trigger such a thing without fission, would not be very efficient.
For "boosted fission" and early thermonuclear bomb designs yes, but not so for the more evolved thermonuclear designs. Navajo (Operation Redwing, 1956) was 95% fusion, Tsar bomba (1961) was 97% fusion, Housatonic (Operation Dominic, 1962) was 99.9% fusion.
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.