Another thought regarding the noise- I saw one suggestion that stuffing soundproofing material beneath the damper plate can help muffle the noises ("Put a sock in it!").
The swifts will migrate in the late summer/autumn, at which time you can have the chimney cleaned and a properly fitted cap installed if you still feel the need. My husband and I have been trying to attract the local population of swifts to our unused chimney for years, and must remove the cap to allow them into that one chimney.
I have access to several professional birders and bird rehabilitators here. If I can search out further info for you Dani, please send a PM. I'd be happy to help.