It seems there are many varieties of the Japanese chestnut, Castanea Crenata. These are the most common, but certainly not all. There are many more.
(variety top to bottom: tanzawa, izumo, oomine, rihei, tsukuba, ginyosei, ishitsuchi, ganne. Far right column is time of harvest. )
Examples of difference in nut shapes:
from:
https://www.ibaraki-shokusai.net/season/season_kasamakuri.php
There is more info about the Japanese chestnut on the Japanese wikipedia page for chestnuts
https://ja.wikipedia.org/wiki/%E3%82%AF%E3%83%AA Ask google to translate into english instead of going to the "english" wikipedia page.
They are mainly selected for differences in time of harvest, nut size, spike length, and ease of cracking. The only mention I can find of difference in pruning resilience is that some varieties prefer, (meaning they will still fruit on that branch the same year) if only two-year-old growth is pruned and not new growth....as far as I can decipher. The vocab used is not readily translated to English...
But, I did find an article in English about the benefits of Japanese pruning techniques from 2000. None other than "The Western Chestnut" published this article outlining the increase in production resulting from pruning.
Pruning Chestnuts for Improved Productivity:http://www.chestnutgrowers.org/2000april.pdf
It seems like any variety would handle pruning fine. The only differences would be in nut production. If a few less nuts aren't a concern, then prune away. I'll be curious to see how the trees deal with training. Please keep us updated in the following years!