Create a gateway or NAT instance

I have an ELB (in EC2 classic) running and one of my client want to hardcode an IP to his firewall rule to access our site. I know that ELB doesn't provide static IP but is there a way to set up an instance (just for them) that they could hit and be used as gateway to our API?

(I was thinking of using HA Proxy on OpsWorks but it points directly to my instances and I need something that points to my ELB because SSL resolution happens at this level)

Any recommendation would be very helpful.