Bring portable generator in through automatic transfer switch

I currently have a portable generator, an inlet, and an interlock on the main panel to backfeed the panel.

I am moving over to an automatic transfer switch with a standby generator. However, as a backup, I am keeping my portable generator and inlet.

I would like to eliminate the interlock and bring the wires from the inlet in through the automatic transfer switch in the same way that the standby generator connects to it, and select which generator I want to use by way of a DPDT safety switch — I already own this one.

However, the only circuit breaker that would be sized to protect the wires between the inlet and main panel (through the ATS and safety switch) would be the circuit breaker inside the generator.

Is that allowable by code? Or do I need to put in a hard-wired single-circuit breaker panel before the safety switch to protect the wires?