A remote (short for remote control) and battery operation are two totally separate concepts. My television set has a remote, but it is not battery-powered; it must be plugged into a wall outlet to operate. My telephone is battery-powered, but it does not have a remote.
A toy that does not require human energy to operate is yet a third concept. It might have a battery. It might be powered by a wind-up spring. And it might plug into the wall, too: my electric train gets power from a wall outlet.
I can't think of any way to paraphrase "battery-operated toy" without changing the meaning, other than perhaps rearranging the words into something like "toy powered by batteries". Why do you want to paraphrase this term?