I have a spinning top and the handle is made out of brass. Keeping it around with me all day results in my hands smelling of brass.
Any way to reduce that effect, or eliminate it completely?
Brass musical instruments are coated with clear lacquer to prevent contact with skin acids from corroding the metal -- and it's corrosion products left on your skin that you're smelling. You should be able to eliminate the smell on your hands by thoroughly cleaning the brass on the top (soft scouring powder such as Bon Ami, a careful rinse, followed by rubbing alcohol or acetone to degrease the metal should be a good method), followed by coating the brass parts with clear nail polish.
This is likely to require occasional reapplication, as the lacquer will wear off due to contact and handling. When reapplying, use acetone to remove the old nail lacquer before repeating all three cleaning steps.