Billing St Canute
I suspect you will have to remove the rudder to get at the prop shaft. I agree with Alan on how to remove the old shaft but the rudder will have to go first.
If you are removing the shaft I would fit a whole new assembly and you can solder an oiling tube in place before fitting. Simple holes in the tube have never worked well for me and let more water in than oiled the shaft.
Not sure why you want to fit an oiler? Judging from your pics its of an age when brass bearings and stainless steel were used so it shouldn't rust and fresh (non saline) water will lubricate the bearings.
Could you drill a hole in the bulkhead behind the motor? Doesn't seem to have any structural purpose and a small hole would let you push/pull the shaft out of the prop tube and fit your oiler block. 😀
Dave