I think the odds of finding NA beer in a beer garden are nil. You may have to brown-bag it if you require NA beer and sidewalk-based people watching? You might think you'd look like a degenerate but this behavior is fairly common, both among some foreigners and Thais alike.

You could order one of the several light beers, and drink it in a glass with ice. Many people do this here: it keeps the beer cold, keeps you hydrated and you consume less alcohol. Most of the beer here is hardly 'craft-brewed' so there isn't much degradation of taste, even with the vaunted Beer Lao, some which I had yesterday with a Nov. 17, 2011 fill date, ack. Oh well, at least it's in a brown bottle.