I don't think you need that based on https://aws.amazon.com/blogs/aws/let-your-ipv6-only-workload...

It's possible that the business model has changed, but at least on this blog they say it's available free of cost.

> Pricing and Availability > These two new capabilities to the VPC NAT gateway and Route 53 are available today in all AWS Regions at no additional costs. Regular NAT gateway charges may apply.

Specifically:

> Regular NAT gateway charges may apply.

Which should say: "Regular NAT gateway charges apply"

Since you still pay for the traffic that is processed by the NAT gateway (per GiB).

That article makes it clear that the NAT Gateway needs IPv4

> The NAT gateway recognizes the IPv6 address prefix, extracts the IPv4 address from it, and initiates an IPv4 connection to the destination. As usual, the source IPv4 address is the IPv4 address of the NAT gateway itself.

If the NAT Gateway doesn't have an IPv4 address it won't work.

Not free of cost, free of additional cost if you were already using a NAT Gateway before they added NAT64 capability.