I have no idea about the modulation. If it is just the case that needs replacing and the internal electrics are still working then I would only buy a case and put the existing electrics and key blade into the replacement case - I have done this a few times on Citroen cars. If the remote just needs a new battery then the car handbook says how to replace it.
Something to be aware of, a replacement will likely not work with the car immobiliser, the immobiliser chip will need to be removed from the old remote and put in the new one but if it is built into the circuit board I do not know how y