Is there a smple way to convert a P type toilet to an existing S type fitting?

Use a McAlpine fitting as they are more reliable. Offer the base of the new pan up to the waste hole. New toilet cisterns can often be shorter in depth so you may have a space between the back of the cistern and the wall. You can fill that out with batten drilled into the wall as support. Depending on that distance use either a 90 degree WC-CONQ space saving pan connector 110 mm diameter (they look like an s, or swan shape), or a 90 degree McAlpine, MACFIT MAC-8L, long pan connector 90-112mm. If the existing fitting in the floor has a concrete lip/collar you may need to chisel or angle grind that off, be very careful. Wedge something in the existing pan whole (newspaper) in the floor to stop the collar falling in.