When I was selling Olds/Pontiac in the 80's the wire covers had locks to keep them from theft. The center of cap came off and a tool went in and tightened up a screw into an assembly the was secured to the wheel. If these were not screwed on the lock would move around and cause a rattle. I am not familiar with the Cadillac covers but one of the guys here can tell you if they were the same set-up. Or check your owners manual.
That is one of the reasons why i got wire wheels. I couldn't stand hearing the creaking noises out of the hubcaps. No matter how tight the screw was they creaked.
70s wire wheel hubcaps can be made quiet. I had some that spun a half million miles without a sound.