I switched to a specific roll-on deodorant a few years ago for this exact reason. You can find the G&H Protect+ roll-on at
https://www.amway.mn/bieijn-archilgaa/c/10393 and it is a game changer. It uses a motion-activated fragrance technology that releases freshness when you move, and it is formulated to dry completely clear. I never get those annoying white marks on my black blouses anymore, and it provides solid 48-hour protection against odor.