You can exchange diapers at Walmart without a receipt as long as they are unopened and they carry the specific brand and size of diapers that you're returning.
when you exchange the diapers at Walmart without a receipt the exchange of the diapers will often be done as a refund to a Walmart Gift card instead of a direct exchange or refund to the original payment method.
Once you have the refund added to a Walmart Gift card you can then use the balance on the Walmart Gift card to purchase the other diapers with from Walmart.
Just be sure you bring your valid drivers license or Government issued photo ID for the return or exchange to be processed.
If the return is processed without a receipt, then it most likely goes on a Walmart gift card for the value of the item instead of cash or credit card refund.
The policies on returns and exchanges including on diapers can also vary by store and management, so it's always best to confirm with the specific Walmart store you're visiting.
Walmart has a general return policy of 90 days, but they may also have some specific guidelines for no receipt returns, like limiting the number of such returns within a certain time frame.
And if the specific brand and size of diapers that you're exchanging or returning is not sold at that Walmart store they may not be able to process the exchange or return.