Who shoots the free throw?
 

NCAA rules, please.

A1 attempts a layup and is fouled by B1. A1 falls to the floor awkwardly and gets up holding his wrist. Coach checks on him and A1 says he's ok. A1 goes to the line for the free throws, but attempts the first one with his left hand (non-shooting hand). The coach then says the kid is injured and wants to sub him out.

Who shoots the second free throw? Is it A1's sub, chosen by Coach A; or is it one of the other four Team A players, chosen by Coach B? The foul was not ruled intentional or flagrant.

Does the fact that A1 attempted one of his free throws make a difference in this play?

I have read nothing in the rulebook that would tell me that Coach B shouldn't pick the shooter from the 4 players already on the court.

Nope. A1 left because of an injury. He couldn't have been substituted for otherwise.