A Panama hat was only one type of a number that we see Charlie Chan wearing during his adventures. Two instances come to my mind at the moment. the first was at the point in "Charlie Chan at the Olympics" where he ans son Charlie, Jr. are on their short-lived fishing trip. Later, in "Charlie Chan in Panama," Mr. Chan is working undercover, appropriately enough, at a Panama hat shop. The style of Panima worn by Charlie Chan was the "Optimo." One of these of GOOD quality is rather pricy, but well worth it, in my humble opinion.
Most of the hats that Charlie Chan is seen wearing are made of felt and were in varying tones from white to grey, to black. These hats had higher, rounded crowns, and the brims were equally sized all the way around (NOT broader at the front). This type of hat is difficult to come by today...but don't give up!