I'm pretty sure they WILL scratch the rims, and almost certain that scratching will occur when ya remove the trim rings. Fortunately, the rings will cover the scratches. I've seen lots of forty year old rims scratched from full coverage wheel covers. The scratches are rusted, but not so as to be unsafe or leak. They would be ugly if ya ran em without covers or trim rings.
So, THERE's the dilemma. Covers and/or trim rings and (hidden) scratches -or - NO covers/rings, and no scratches..... AAaahhhh - - decisions, decisions......