The class feature "Unarmed Combatant" requires that the monk have a hand free to make use of their Unarmed Strike. That's the only thing that requires the free hand, IIRC.
So, that means that the aforementioned dagger/sling monk wouldn't be able to make use of the Unarmed Strike, so basic attacks would have to be made with the dagger, rather than the beefier fist o' fury. If you're not making that many basic attacks, it's not a big deal.
SFAICT, you could have a club in your off-hand to use with Crashing Tempest Style and (with Quick Draw) be able to fling out a shuriken or dagger for Starblade Flurry, and still get to use your Unarmed Strike.
Brad