If they inquire, say, "I don't drink."
If they inquire further, and ask why not, say, "I just don't."
If they inquire still further, stop going to the happy hour.
There should be nothing mandatory or semi-mandatory about social drinking. I imagine you are feeling some pressure about being the new person, but they can't make you drink, they sure as heck shouldn't be making you go to happy hour.
Good luck, be strong, and stick to your line, "I don't drink. Period."