Most likely not, as that is the sort of specific and important thing that would have been mentioned along with Sleight and Disable.
That said, the TK Finesse talent needs some serious clarifications in many different ways. I started an FAQ
http://paizo.com/threads/rzs2sw4a?FAQ-RequestHow-does-Telekinetic-Finesse-w ork#1
Our "ruling" for this question was "yes you can". However, since the only thing that Telekinetic Finesse gives you is fine manipulation, and since it is in no way linked to Basic Telekinesis (or more importantly, Telekinetic Haul), your effective Strength level is 1, which allows you to apply up to 10 pounds of pressure max, as per the Carrying Capacity table (enough to open locks and lift a pouch off someone), which means that all attacks from the weapon is at -5 damage and -5 to attack (minus additional penalties for being remotely controlled of course).
Yes, but not worth it.
Can you wield weapons without using your hands with this feat, using telekinetic force?
This is already what telekinetic blast does.