Ordinary balloons are formed from liquid rubber (latex). Helium balloons are a form of metalized or "foil" nylon, not Mylar (boPET) as people often mistakenly call them.
Based on atomic size, I would surmise that the larger H2 molecule would effuse at a slower rate than the smaller He atoms. The issue of air densities could pose a problem for the structural integrity of your balloon, but the difference between H2 and He should be negligible (for what you are trying to accomplish).
To specifically answer your questions, yes, a balloon normally used for He should work, and your local party supply store should sell "Helium" balloons - though they don't necessarily have to read 'Happy Birthday', I would, however, keep the birthday candles away from them.
I hope this information was helpful...