Bismark, Althenick,
In broad terms, I doubt that the costs for the day to day running of the fleets i.e. the aircraft, training, fuel costs etc would change drastically, and in that sense it should be cost neutral.
However, if the RAF were to cut all RW capabilities across to the other services, there would no requirement for the RAF to maintain funding for Benson and Odiham and their personnel - remember that although JHC is in the Army chain, single service Full Command issues and responsibilities remain in place. Plus you would have to find funding for any other capabilties associated with aviation e.g ATC at JHC units, TSW, fire and crash provision, support / R&D currently provided from within the Air domain e.g. AWC type support, recruitment of and training for long term personnel sustainability (air and ground crews) plus dealing with the fallout from those that refuse to change service and walk etc etc. All of these are crucial elements for ops that have to continue to be provided to allow the ac to continue to operate and many of them are not provided outside of Air.
Actually rebadging the cabs and calling it JHC Benson, Odiham etc is one thing and you probably wouldn't notice much change in the short term (maybe a bit more grumbling from the crewmen and the neighbours when they realise they are now living next door to an Army unit
). But longer term, trying to sustain such a capability when you take all the other aspects that are provided by elements outside of the Army / RN into consideration, that is where the costs will come into play and bite the Army and RN. Cutting RW across to the end users is one of those ideas that is deceptively simple on the surface but would have significant structural issues for each of the services and as such comes with the caveat of be careful what you wish for stamped all over it in big red letters.
That said, and before the black Omega turns up outside the house to ruin Boxing Day, this is all just Melchett's opinion based on previous experience in JHC - I honestly have no idea what is going to happen to Puma, or any other longer term JHC structural issues. I may have some prior JHC experience, but I'm still a peasant way down the information food chain.