OP did not sign for the new charge. I'd pay the previous balance and not pay off the $400. The ex signed for an item, let them pay for it. If they don't - oh well. He is the primary cardholder and they will go after him first anyway. If he doesn't pay it, I'm shrugging but there's no emoticon for that!. To each their own but I'd take a $400 hit on my credit. I'd explain it away with the credit reporting agencies and provide the documentation from the CC Company that confirms the signature of the party that charged the item. For a $400 item? It's really not going to be an issue.
On the other hand, I'd pay off the balance I owe or transfer it to another card as soon as possible and then ensure that the statement address is changed to that of the ex. Will be difficult for him to argue anywhere that it is the responsibility of the OP to pay it off when the item was charged after the divorce.