Red rosin paper is a much better option to use if you are wondering how to protect hardwood floors.
How to protect hardwood floors when moving appliances.
The scuff shield or appliance mat refrigerator is placed directly underneath the appliance and acts as a shield to protect the hardwood tile stone or vinyl flooring against scratches indentations gouges and or roller marks that might otherwise occur during the moving of an appliance.
Whether you have hardwood floors laminate carpeting or tile you can protect them from dings dents and rips if you approach your appliance relocation challenge armed with a plan and the right tools.
Spread the second blanket rug or cardboard box on the hardwood floor next to the box.
For future moving jobs keep in mind that a dirty floor is a damaged floor.
Dirt and grit under the foot of an appliance can increase the friction enough to rip vinyl pretty easily.
Scratches and dents avoid walking on the floor while wearing high heels spikes cleats or other shoes that may cause indentations in your wood flooring.
So cardboard is okay for a quick fix like sliding it under a heavy appliance that needs to be set down but other than that it is not really a great solution.