The best non-medicinal thing I've found for it is coconut oil. Since it's edible, it's about as safe as you can get. I'd probably put it on him at diaper changes, 3 or 4 times a day. The Dr. recommended Aveeno, which probably worked better, but her rash was so inflamed that creams stung... the coconut oil doesn't sting so it was a lot easier to put on my daughter. Coconut oil has some antibacterial properties, so it helps prevent infection when the rash is open. It's not a miracle cure, won't make it go away but it definitely helps keep it under control.
If you do have to get a medicinal cream, try putting it on when he's asleep to give it a chance to absorb into his skin before his hands go in his mouth. I put socks over my daughters hands/up her arms to keep her from scratching in her sleep... maybe that would work to help him keep his hands out of his mouth.
When you see his start to scratch when he's awake/in your lap try patting the area for him, closer to his trunk than the itch. The tap-tap-tap of your hand can disrupt the nerve that are signaling the itch, and make it stop temporarily. If you're in an area where you've recently just turned off the furnace, you might notice an improvement in his rash... heating systems make for really dry air, so a lot of people get some relief from eczema in summer months.
My daughter often has a flare up of eczema right before she comes down with a cold. It's something to keep in mind during flu season, another reason to be diligent about hand washing/all the avoid getting sick precautions.
It's such a frustrating experience! I'm sorry I don't have a great miracle cure to pass on, my daughter still gets patches of it behind her knees and the insides of her elbows.