I can tell you a good way to rid your hat of some of that smell....buy some french vanilla coffee, put some in a paper cup like what you use for cup cakes...put you hat crown side down in what box you store it in...CAREFULLY place your cup with the coffee ground in the center of your hat with your hat in a hat box...and have the hat box someplace like a counter top or table so you can slide the box with the lid on it, into a large plastic trash bag and do not spill the coffee grounds...then close up with out moving the box around, close up the plastic bag with a twist tie. Let is sit for at least 24 hours...your hat will smell real nice...and the coffee will have absorbed any "stink". I do this to vintage hats that have that nasty strong musty smell.....it works every time for me and no complaints...just do not spell those coffee grounds in your hat or they will stain it badly!
I would go for Cindy's coffee-trick. It's been tried with very good results by several loungers. Crumpled newspaper pages packed around and inside the hat in a plastic bag also works on bad smells. You may try both - maybe with a few iterations over the processes. Hoping for a good result ...
Thanks. I'll give it a try.
If you want a serious answer. You could always use scotchguard to protect the hat from getting wet. If it can't get wet it won't smell.
I actually did use Scotchgard when I got the hat last year, at the suggestion of the hat store. I've never done that with an Akubra; I believe they are already treated with something, and in any event they seem pretty impervious to weather. I think the current version of Scotchgard isn't as effective as the original, but it's also apparently not as toxic. Seems like a fair tradeoff.