Is my solution to this puzzle reasonable?

Additional comments.
The paper tape is very useful. Consider that you can quite accurately make it divided evenly with folding and such. Helps in the latitude estimate.
I personally took the time to measure that from the tip of my middle finger, to my elbow bone is 50 Centimeters. So I have a basic measure with me at all times.

It doesn’t matter what units you’re using; all relevant measurements you’d be making would be ratios, anyway. If the noon shadow of the water bottle is 1/3 its height, it doesn’t matter if that’s 3 inches and 9 inches or 5 cm and 15 cm or 2 fingers and 6 fingers.

Not sure if you are replying to my post about 50 centimeter forearm comment. In the context of the riddle I specified that it is an estimate of percentage difference. The paper tape with a lot of evenly spaced fold marks would make the estimate better.

Yes, but while knowing the length of your cubit in centimeters has plenty of practical applications in everyday life, it happens not to matter for this particular situation. Marking off tick marks on the paper would let you make measurements in paper-ticks, and you don’t need to know how to convert those to centimeters.

Here is a thread from another board discussing using the shadow length at noon on an equinox to find altitude. It includes illustrations.