Free-flying robots have the potential to autonomously fulfill a wide range of tasks involving manipulation of objects in space. In this paper we study the design of a wrist mechanism for free-flying robots that are equipped with an adhesive gripper for attaching to objects and surfaces. The wrist and gripper allow the robots to apply moments in addition to forces, which increases their versatility for object manipulation. We apply grasp optimization to establish limitations on the forces/moments that the wrist can impart, subject to adhesion capabilities. Building on these results, we present considerations for tuning a passive wrist mechanism, or controlling an active wrist, to broaden the range of forces and moments that the robot can exert. Our theoretical insights and wrist designs are validated in simulations and on a planar micro-gravity test bed.