Many years ago I experimented on a 3.5in 1.44MB floppy disc with a mains powered tape head demagnetiser. It had no discernible effect and data could still be read back on a PC. When I clamped the disc between two permanent magnets removed from a motor and rotated the disk by hand, all the data vanished.
Don't worry about the CRT degausser, but don't place magnets too close to the platters inside your HDDs. Even if your degaussing coil was powered on, provided it wasn't lying on top of the drive, I doubt if it would do any damage. There are magnets already mounted inside drives, but they're carefully positioned so as not to affect data.