Is there a standard size shaft that works with a range of economical water cooled motors?
Pretty much all shafts sold are a "standard" size, or fall into a range of standard sizes. The props have a matching range of standard fixings (screw thread retained by a locknut or dog drive). For connection to the motor shaft, you get the appropriate coupler with a hole at one end to match the prop shaft, and one at the other to match the motor shaft. It could be a solid coupler, it could have a joint. If this standardization was not the case, there couldn't be a hobby industry where there was a range of manufacturers for the various parts in the chain.
Solid shafts, I have experience of, but have not used flex shafts, so it will need the knowledge of .someone else to get a good answer there. But having seen a few, they are generally high maintenance items - they do need attention after every session and even then, have a shorter life expectancy compared to a rigid shaft fitted with lubricators.