What is your custody agreement?
If you do find you have any suspicion that he is drinking later on, you can always pursue the full custody agreement or have a soberlink clause put in. For now, what can you do, you have zero proof really.
I totally understand your worry, don't get me wrong, but what can you do with no proof?
Since he is just white knuckling it, all you can do is be vigilant in observing him during drop off and pick up.
How old is your child?
Are there family members on his side that he has any communication with at all that you trust?