I also recommend using the Car Seat over CARES Harness.

Rather than buying a CARES harness, I would get a cheap, lite weight car seat from Walmart, especially if your current model is a heavy and durable Britax or Graco. The Cosco Scenera is worth a look at.

I have used CARES Harness, Britax car seat, and Evenflo Titan Elite car seat onboard the aircraft. The Evenflo Titan Elite was the easiest to install onboard/rental-car and allowed for the Britax to remain in the car for the drive to and from the airport.

CARES harness was a good idea in theory but my daughter was much more comfortable in the Titan Elite. Another installation problem with the CARES harness is that it requires you to loop around the child's seatback. The setup is not hard but requires the cooperation of the person seated directly behind the child. Sometimes that cooperation is not forth coming.

Either the car seat or the CARES harness can raise questions with the FAs. In the event the FA has a concern, request they consult their manuals and the captain to ensure they are in compliance with airline regulations. Also before going onboard with any restraint devices check the location of the National Safety Mark for your unit. it will have CMVSS 213 or CMVSS 213.1 embossed on the restraint device.

Pro tip. Early board with silent boarding and show the national safety mark to the first FA you see at the aircraft door. Once the FA gets their questions answered ask them to join you after boarding is complete at your seat for a quick demonstration how to remove the child in the event you become incapacitated.