2A should be fine on a 737. I'm sitting in 2E on a 739 right now, and can see both 2A and 2F have plenty of underwear space. 2C and 2E (the aisles) have bars in the middle, so the carrier will need to go sideways in the share space between the aisle and window if possible.

Not sure if it's the same on the 738s, but IME the window seats are usually fine in F.