While we don't know the exact process that will be fastest, here are the most likely based on last year.
1. You ordered from AT&T, you just call Customer care before you activate the new iPhone 5 and the rep switches the pre-assignment of the new Nano-SIMs ICCID and the IMEI of the iPhone 6 from your main line to the line you want. Then you activate the new Nano-SIM and it works on your correct line.
2. Worst Case, you activate the Nano-SIM and iPhone 5 on the main line, this kills the current SIM on that line and also breaks the voicemail and adds a data plan. You go to an AT&T Corp retail location and they fix your account, provide you two new SIMs: new SIM for the dumb phone and a new Nano-SIM for your iPhone 5.
Did you order from Apple, there were different steps?
Dave