The electric scrapers that Glenn Janie is talking about are used over concrete flooring, but I'd be real concerned about what they'd do to a much softer hardwood floor. I'd be concerned that an electric floor stripper would make match sticks out of it.
What I'd do instead is see if either water, mineral spirits, lacquer thinner (which is mostly toluene, or acetone) will dissolve the old adhesive. If any of them do, then put down some solvent over an area and immediately cover with wax paper to prevent the solvent from evaporating. As the solvent penetrates through the cardboard to the glue at the cardboard/glue interface, it will soften the glue at that interface making the cardboard easy to scrape off the glue with a putty knife. As the solvent penetrates deeper and deeper into the glue, it should make the glue easier to remove by scraping with either a putty knife of paint scraper.
None of the above mentioned solvents will harm wood. (Water will make wood swell and possibly raise it's grain if there's no wax or polyurethane over the wood.) Mineral spirits won't harm polyurethane, but the other two solvents will etch polyurethane and probably dissolve Carnauba Wax. But, in all liklihood, you're going to have to refinish the hardwood anyway.
I'd try removing the cardboard and adhesive in the vicinity of the kitchen sink first. That's the area where the hardwood is likely to be in the worst condition, and that's where you're probably gonna most need refinishing.