Maybe just have a talk at pick up. "Hey dad, I just wanted to talk to you about Jack. He is so doing well here and is super busy and has a great time! Since we are so busy, he could definitely use a bath each night or at least a rinse and fresh undereear. You know how kids his age are...they get stinky real quick lol! If you don't have a washer and dryer at your apartment I can definitely wash his clothes if you need, so just lmk if I can help in any way!" Or something similar. Like Cat said...make him aware that YOU are aware and then give him a chance to handle it. And I don't go along with the idea that men aren't capable of keeping their children clean and need to be taught. If anything, the men I know are more clean and hygienic than the women I know!
Because his time is limited with his child, I can understand him being kind of intimidated by the process, but parenting means that you work through the intimidation. You are the parent, they are the child. You have to do what's in their best interest, even if they don't care for it.