Well if it's mainly to keep the rain off the deaf-aids then maybe a souwester?
Only half joking as I have considered buying one, but more for hillwalking and such as wearing it to the shops might look a bit silly
On a more serious suggestion I too like the recommendations of a pork pie hat (which I'm half tempted to get myself) whether Thelonius Monk jazzman style or the two tone ska small trilby style . Not so keen on old-man trilbies. The Homburg idea is good too, and much more cool than a fedora.