There are contact cleaning solutions made specifically for electrical contacts... If you search on Amazon specifically for "electrical contact cleaner"... you'll get many hits... most are spray cleaners and should be used very judiciously... IOW, spray on a rag or q-tip... and rub the contacts... Don't spray into the contacts or camera... There are also pen style cleaners in the same search that are like small hard rubber/abrasive erasers... Again, be very careful as they abrad small particles are released, which you don't want to get in your lens or camera... Get one of the camera rubber bulb blowers while you're at it to blow out any dust while you're cleaning... I'd probably start with a microfiber cloth wrapped around a small stick/blade and dipped in a bit of Isopropyl alcohol to just wipe the contacts before moving to the other more serious solutions...
Good luck...