The dust cap shouldn't affect the sound. Use blue tack or masking tape to do what you can.
Otherwise, there are speaker repair companies that can cut off the old caps and glue on new ones: Tri-state loudspeaker in Aliquippa Pa is the best I've seen.
Otherwise, there are speaker repair companies that can cut off the old caps and glue on new ones: Tri-state loudspeaker in Aliquippa Pa is the best I've seen.