1/8" drill into center of bung down to screwhead. Take a #10 screw and screw it into the hole. It will bottom out against the screwhead and gradually lift
it out. Go slow and hope some wiseguy did not decide to epoxy them in place. If they are epoxied, it will lift/splinter the surrounding wood. If you are lucky, the handrails are screwed to the deck rather than thrubolted (although bolted is better).
My boat has an interesting arrangement where a handrail below matches one above, screws from inside handrail go thru the deck and into the topside rail. Pretty slick and no bungs, but a challenge to install solo.