I would not consider using a nearly 10 volt battery to drive a 6 volt motor spinning a paddle. If it doesn't break the paddles or gears, it will probably cook the motor. Or the wire. It all depends on what the weakest link is, but applying excessive volts with the ability to deliver the current demanded will find it.
As a general rule, transmitter batteries are not intended to deliver heavy currents, I wouldn't drive anything heavier than a pair of lightly loaded servo motors or CD drive motors. If the paddle motors are anything more than 140 size, you are into the "grey" area.