how web page replay via web proxy?

I use a web page recording tool recorded some websites. and I can replay these by chrome mapping http/https ports to this proxy.

I wanna replay these websites through a web compression proxy.But this web proxy also need chrome mapping http/https to this. That make a collision replay tool and web proxy. Either use replay tool or use web proxy.

So, how I can replaying websites by
replay tool -> web proxy -> chrome?