>>/24741/
 >>/24743/
Sorry, nor sombrero neither panama hat is characteristic Swedish hat. You can have a knitted one similar to Norway's. I thought about a Vendel era helmet but those types that cover the "face" (the colors) of the ball ain't good.
If you can come up with a hat that is typical for Sweden, or maybe one that a famous Swedish person used I'll gladly try to draw it.