..... if you both plan to log the time one of you would have to be a CFI.
Both logging the time isn't the issue. If you do the flying, you're entitled to log the time. Insurance/contract with the radio station don't affect that.
Insurance and legality would depend on the insurance policy and the terms of the contract with the radio station.
Is it a commercial or private flight? eg Is the operator being paid to fly the helicopter or to provide traffic reports by whatever means he chooses?