Thanks for the reply--and to the others who did, as well. It's not a leather-y smell that bothers me; it's a chemical-y odor that is causing irritation in my upper chest/lungs when I wear it. Strange...
Thanks for the ideas about Mono straps, guys. I'll check around for them...
My Fender P bass came in a fabulous SKB flight case that stank to high heaven of some sort of chemical . Probably glue. Anyway, I slapped a dryer sheet in there and it mitigated things drastically. Maybe try something similar?