When repowering, most people will size the engine comparable to what they had before. Changing packing boxes, shafts, props ext can get expensive. That being said, it probably original running gear
or at least size.
You're on the right track, measure with calipers. 3/4 is about the smallest shaft you would run but seems fine for a 27. 1 1/4 seems way overkill.
I've had good luck with boatzincs.com