I leave the unopened bags of perique at room temp. Once I open a bag, it stays in the fridge, as I gradually remove some leaf (8 or 10 at a time) to dry-down and shred. It is definitely stinky while drying. Once dried adequately, I store it just like any other pipe blending ingredient.
Decades ago, the tin aroma of pure, bone-dry, St. James Parish perique included a subdued barnyard hint. I have never noticed a barnyard scent in any of my perique pipe blends.
As for stinky pipe bowls, if I smoke any Caribbean-type cigar leaf or most (even lightly) cased commercial blends, then the bowl is noticeably stinky afterwards. That doesn't seem to happen with Little Dutch, Ohio Dutch, PA Red, Long Red or any of the PA Broadleaf/Seedleaf cigar leaf varieties.
Bob