The Swiffer wet jet is okay to use for hardwood floors but only when using the wet or dry swiffer cloths for cleaning the hardwood floors.
It's not recommended to use the Swiffer Wet Jet Spray solution on the hardwood floors though.
A good natural way of cleaning hardwood floors is to add some vinegar to some mop water and mop the floor with the vinegar and water.
Be sure to thoroughly dry the hardwood floor and don't leave wet spots on the hardwood floor otherwise you risk cracking and warping the floors.