Hi Chiro75-
The whole problem of "strap stink" is something with which watch fans have wrestled for years. The traditional wisdom is to simply stick with a metal bracelet that can be immersed in lukewarm water and scrubbed clean with mild soap. Humidity, temperature, and body composition leads to a finite service life for many different strap materials.
Soaking leather will drastically reduce its lifespan and contributes to an even stinkier band in the short-term. If you prefer leather, try to swap between different watches so the leather can completely evaporate between sessions. The inside can also be treated with corn starch to soak away oils and smell. Be especially gentle with crocodile bands, which are generally found on the dressiest of watches.
The other option is to go with the newer kevlar bands, which look a tad nicer than nylon or rubber and can also be soaked n' soaped. They are very durable and are available in a wide variety of colors. Good luck with your search.
~ Blue Jays ~