The friggin' cable we suggested costs maybe four dollars, man.
If you don't believe us, then invest four simoleans and try it for yourself. If it doesn't work, take it back and get your friggin' four dollars back!
As for the sub splitting out the highs, RTFM that comes with whatever sub you wind up with. There's your "definitive" answer.
You didn't ask about a splitter before, but you don't need it for the implementation you stated.