The child would likely be sent off to the monastery. See here. He might be sent off to the monastery even if he was physically fine but was just a younger son.

However there's always the possibility that he wasn't and just plodded along. Date Masamune was blind in one eye and still carved out the third largest non-Shogunate realm for himself by the end of the Sengoku. And there are always other work besides fighting that needs to be done. Yamamoto Kansuke was also blind in one eye and might have had a limp, but was recommended to Takeda Shingen as a rōnin skilled at building castles, and became an important strategist for Takeda Shingen (if you believe Kōyō Gunkan anyway).