I'm no expert on canker, but I'm not 100% convinced it is canker - could just be split bark which is better news and may be due to the amount of rain we've had this year (or some other stress factor). If you think that you're going to lose the tree anyway then it might be worth waiting for a dry day (ha ha!) and cutting around the lesion with a Stanley blade then cleaning out the dead material and letting the tree scar over naturally. If it's canker then you're likely to see discoloured cambium and you'll just keep enlarging your area of 'surgery' until you get to the healthy cambium. If it rings the tree then it's a gonner unfortunately. If it does ring the tree as a last attempt to save it then you could cut it back to just above the scion and it could well sprout again - if it is canker and it's gone all the way to the scion then it's as good as dead anyway. Having said that please don't do anything drastic based only on my 'advice' - greengages are my favourite and I'd hadt you to do anything unnecessary.