I think there's some confusion here. When most people refer to cleaner shrimp, they mean scarlet skunk cleaner shrimp, Lysmata amboinensis. Occasionally, they mean fire shrimp, L. debelius. This refers to the habits of picking parasites off of fish. Neither of these will bother tube worms & feather dusters.
Sometimes people get peppermint shrimp, L. wurdemanni as part of a "cleaner crew". These fish do not take part in that symbiotic activity that gives the other shrimp the name "cleaner" but they can be used for scavenging and picking off unwanted animals such as small pest anemones, polyps, and yes, tube worms.
This is the problem with common names, sometimes.