Is Starry Form Archer hands-free, or I can't use it or attack if I have something in my hands?

The text of the feature doesn’t require any use of hands, so I guess you can make the attack with hands full. 

I would choose something flavorful for describing using the attack with full hands though. 

It doesn't explicitly say that the archer attack uses hands so yeah you can use it with stuff in your hands. I guess the implication could be that the attack stems from the constellation on her body