I'm using a science bridge officer with the Jam Sensors skill. Each time I invest a bridge officer skill point I can clearly see the recharge time decrease in the tool tip for this ability.
Also on the tooltip it lists skills which effect duration, including Starship Operations. However, when I invest my captain skill points, I do not see any change in the duration. It remained at 10 seconds from the time I had zero all the way up to nine points in Starship Operations.