Cardboard is quite abrasive. Imagine rubbing twigs on the shiny parts of your bike.
But I suggest you have better things to do than fret about a scuff or two. Based on my insufficient experience in riding the interior and the coast of British Columbia, you might better use your time to collect more scuffs.
Ride the Sea-to-Sky up past Whistler, and take care on the one-lane bridges. When I went that way a few years ago, northbound traffic (me) always yielded to southbound traffic, and there were always curves just north of the trestles, so the bridges were a bit scary for me.
Go west from Victoria, and realize near Sooke that you are actually rounding a corner of the country, and everybody in Canada is to your right. Then ride across the island to Duncan. You will totally forget about scuffs.
Ride today. Buff and polish in the late fall, and enjoy remembering "That mark was from a branch near 100-Mile House ... idiot near Jasper dropped his lighter on my fairing and left that chip ... etc."
And me? Next week I leave Florida for Toronto and points north. The bike will
get some cleaning before I go, but none more until I complete the voyage.
Enjoy your ride, with or without my buttinsky advice.