[FrankenMauser]

Printer/Copy/Writing/Tracing/Drawing/Sketch paper -basically any paper with a 'finished' side - has abrasives in it.
It will slowly remove bluing.
It will, however, take some time.

Paper towels, toilette paper, and 'raw' finished cardboard generally doesn't have much in the way of abrasives in it, other than contaminants - unless it was made with recycled materials.
It shouldn't be an issue when used as you described.