I broke my thumb in college back when I was a runner, and I am a heavy, heavy sweater (think looks like I jumped in a swimming pool after a trainer session). The only thing I did for mine was make sure I tried to dry it out well after a workout, by putting my hand in front of a fan or using a hairdryer.
I was also really paranoid about how badly it would smell, so I put some baby powder down into the cast…which was a terrible idea!!!
In my injury prone experience, casts are going to smell after a few days anyways, so just train away!