Boil a little bit of water on the stove. Have your old swiffer solution bottle ready, as well as a sharp knife or scissors.
Take your sharp knife, or scissors, and cut off all those little tabbies all the way around the cap. This will convert it to a normal twist top cap, so you only ever have to do this once! Then, rinse out your bottle, and fill with your own cleaning solution. I have hardwood and like to use water & vinegar, and my second bottle now holds water & Simple Green. I would keep the solutions liquid (like don't add baking soda or something), just so that it shoots out the sprayer nicely and won't get clogged up.
Hope that helps you! Don't throw away your next few solution bottles so you can try this yourself!