in a perfect world this would be great, just be aware that there is a very good chance that the dimensions of the bike may not allow you to get it the same as your bike. At any age, having the bars just that much too forward, or too low, and I'm talking a cm or half an inch, could very well present itself with your neck issues. Heck, I'm over 20 years younger than you and wouldnt want to take the risk of a not well fitting bike for such an expense of a trip, only to not be comfortable riding.

another point to bring up--lets say a rental bike does fit you well, if the gearing isn't low enough for carrying a few panniers or more of stuff and going up hills a lot, then that will very possibly bring in knee issues or other 83 year old body stuff--not fun.
At least you know what gearing works for you from your trip ten years ago, but all the older folks I know have told me for years that every decade has real differences in fitness and strength, so I'd be very aware of gearing and risking having a bike that has too high gearing--no fun at any age if very hilly.

Perhaps a moot point if you follow a route along canals or rivers, but something to be aware of if you are being responsible about foreseeing issues that could very well be a factor.

If you are not planning to bring camping gear, and are a good packer (your hiking experience etc would support this) then your pannier load could be rather light, a help with hills etc, but again--these are details that only you can assess, and hopefully be pragmatic about being no longer 73 and taking that into account, at least for planning daily distances.

oh, another point, travel insurance for any medical issues while on tour. Being over 80 will probably mean an increased cost, but proper research will give you answers.