What kind of books do you think Shiro likes?
I think Shiro's taste are mostly going to run towards non-fiction. Mainly very long books about war and political history.
As for fiction books I admittedly haven't read many books by Japanese authors and the ones I have read I'm not entirely sure Shiro would enjoy. So I'm going to be relying on the Internet for some of my answers. Apologies if I end up getting something wrong.
I don't think his Uncle Tomo prioritized academics in his childhood but I do think he would've made Shiro read The Tale of Genji. A book I actually do know a bit about because I've read several books on it's author: Murasaki Shikibu.
The Tale of Genji isn't just considering Japan's first novel, but the first novel ever written. A point of cultural pride for several people. At a whopping 1, 216 pages it tells the story of the adventures of a prince named Genji during the Heian period.
Works I think Shiro would seek out on his own would be Rashōmon a short story by Ryūnosuke Akutagawa. The Book of Five Rings by Miyamoto Musashi. No Longer Human (also known as A Shameful Life) by Osamu Dazai.
Despite this not being a novel written in Japan; I think Shiro would benefit from reading Japanese Gothic by Kylie Lee Baker, a Japanese-American author. As I think he would find himself to relating to the character of Sen.