Cardboard sucks because you feel every rock and lump that is under it. Start with a good grade of plywood and lay the correct side down. You won't get any splinters. A good thickness allows one to drive the car on it and makes an excellent "driveway" for repairs. I use my ramps, jacks, stands, etc without issue.
If splinters are still a fear, lay a tarp down as well.
As for the seal problem, change the bearings as well. It is not a hard job at all, just messy and a little time consuming. The tool to pull the bearings can be "borrowed" from most any parts store but if you have a harbor freight near by.
Be prepared to find a bad axle shaft. If you do, do not waste your time with repair bearings or any other sort of band aid.

If splinters are still a fear, lay a tarp down as well.
As for the seal problem, change the bearings as well. It is not a hard job at all, just messy and a little time consuming. The tool to pull the bearings can be "borrowed" from most any parts store but if you have a harbor freight near by.
Be prepared to find a bad axle shaft. If you do, do not waste your time with repair bearings or any other sort of band aid.