Just order what you want to drink. If you wanted to, just order one drink and take your time with it. I don't know your tolerance level but one drink should be fine.

If you don't order anything alcoholic, don't sweat it. Just tell them that you didn't feel like it. They don't need to know more than that, and it's also not a lie of any kind. You don't want to drink that evening. That's not an issue!

Although... going specifically out for happy hour? Unless there are also deals on appetizers or stuff? Happy hour usually means alcohol.....