Any counter is fine even the ones reserved for military, etc. While you are not supposed to use these, you just act like you can't read Chinese. I always just line up in the shortest line and my girlfriend lines up in the "proper line" just in case.
"Just tell the rep at the counter that I have a confirmation number and they will know what to do?" - no need to tell them anything, you hand over your passport and the confirmation number and they know exactly what you want. You can show the number on your phone or have it written on a napkin.
If you are traveling in some cities around Shanghai, you do not even need a paper ticket anymore.