I'm not going to claim I know the answer, but I do love a bit of math...
I think you want a band that will come as close as possible to having the same perimeter so that when you deform the band it will fit on the oval stem. If you approximate the oval as an ellipse, you can calculate an approximate
perimeter. Using your numbers and the first formula here: https://www.mathsisfun.com/geometry/ellipse-perimeter.html
I get perimeter=39.91
Then using the circle formula I calcuate the circle diameter that will give that circumference:
D=C/pi. D=39.91/pi. D=12.7
So the diameter you want is 12.7 mm (assuming that you are not going to decrease the diameter of the shank to fit the band). If you only have a choice between 12.5 and 13 mm, I personally would go with 12.5 and sand the shank a bit to get a perfect fit.
I hope that helps, or at least provides some entertainment
Please let us know what you choose and how it works out.