[Ellie May]

Any cleaner has the potential to do harm because they are chemicals.
Swiffer seems to carry the same amount of danger as other cleaners (see Snopes). Just make sure the floors dry before letting the pups walk on them. If you are still worried, maybe you can use something more natural.

I use Mr. Clean, Clorox Clean-up, 409, Fantastic, Pine Sol and Swiffer and have never had a problem but that doesn't mean that they are safe either...