Public subnet & Private subnet on different interfaces, with NAT

[ionutul]

Hello!
I've attached a short network diagram that would better explain my needs, but I will try to also write and explain them:

At this moment, I am using a private network the IPs from the local 10.20.0/16 network on the ax0 interface and just creating a NAT entry for every IP/subnet I'm trying to access. (example: 10.20.0.20 -> 1.2.3.20) that the ISP is routing to me through the WAN static IP they assigned.

My goal here is to create a new network on ax1 and be able to freely assign an IP from the public subnet (1.2.3.0/24). Their advice was simple: disable NAT and just assign the subnet to a network and it should work.

I cannot do that because I can't change the configurations of the whole legacy machines (that are assigned 10.20.0.0/16 IPs with NAT)

I have created a new network on the ax1 interface and configuring it with the public subnet would not give me internet, but if I configure it with any other private network (RFC1918) would work without any issues.

Do I need to disable NAT for the entire router for this setup to work? I need both a private network (ax0) that I can use internally with some NAT entries here and there for public projects and a stictly public network (ax1) that I can assign public IPs to the new machines. I can also work with an alternative to NAT, that would translate the address from the private network (ax0) to the public network (ax1)

Thank you so much for the time you took to untangle this mess of a setup and for every answer!