Originally Posted by Drip

I think he wants some control over what allies are in the list to use as helper squad.
And I'm not sure there is. Last log-in time seems to have some effect on the list, but there also seems to be some kind of "cooldown timer" for a helper squad after you used it, making it not appear again for about 15-30 minutes.
So, your best bet to get a specific helper squad, would be doing a couple of 1-1 runs (lowest stamina, skip any SG that might appear) until your desired helper comes on the list, and then do the map where you want to use that specific helper.

You don't have to actually start any mission to see which helper squads you can choose from. Just looking at the "Choose Helper Squad" screen will help you with that if you really need to look for a specific squad.

To get out of that window you can click on any of the buttons on the left side in the game.