In a few weeks I'm embarking on a 2 month trip across Australia and New Zealand. I don't know for sure but my impression is that these places are way sunnier than where I live (Midwest USA) so I need to get a serious hat as I feel the standard trucker cap won't do.

The thing is though, I'm bald and I don't want it to look like I'm coping or trying to cover up, and I have no idea what kind of hat sends that message. Panama hats seem the most universal but I don't know. What do you guys suggest?