Although Tritium does produce ionizing (beta IIRC) radiation, it's pretty weak compared to most radioactive materials. Typically you ingest it as tritiated water, but you can also breath it. As long as it's not in your body pinging around in your tissues, you should be relatively safe. Don't go breaking it open and eating the stuff even if it leaves your body in about a month... <img src="/images/graemlins/smile.gif" alt="" /> If it does break open, handle it with chem gloves and dispose of properly. For the most part don't handle it, breath it or ingest it, and it shouldn't pose any problems in it's sealed tube.
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Experience is a hard teacher because she gives the test first, the lesson afterwards.