You might try going with a 12-34 or 12-36 cassette, just to be on the safe side. Changing a cassette is easy and cheap. Changing the gearing up front, not as much.

Generally speaking, I like a 1:1 gear ratio (34 front - 34 rear, for example) to be my second- or third-lowest gear. I wouldn't do a tour on a bike that doesn't even reach that point.