The wireless one will have a receiver which would then get wired into the system - it'll just make the original wire redundant
EDIT: Just to add, if you were willing a drop a little extra cash and get a modern hot water tank too, it's likely it'd come with a slight rejig of pipes allowing for a modern boiler that will do load and/or weather-compensated flow temperatures for radiators (lower temp = more steady heating, more efficiency, more comfort etc) and PDHW (priority domestic hot water) which would then increase the flow temperature up to 60-65ºC to the hot water tank only to top it off, then go back to heating the radiators at the lower temp.