I've wired the channels together in parallel already.
You asked a question....
When I'm programming this, do I need to program both channels to get the full 4A out, or will the motor shield pull the 4A on its own as it needs if I just program one channel?
Here is the answer... Did you read this ?
What does it say next to the label "Figure 7" at the top of the page ? (yes I know it's from the L298 datasheet and your motor driver uses the L293. )