Turn off client auth if uri equals

The problem here is you want to make layer 7 decisions on something that has happened in the past. The SSL connection has already been negotiated. My recommendation is when you make your decision, redirect them to virtual servers which have the SSL setup the way you want it.

when HTTP_REQUEST {
  if {not ([HTTP::uri] eq "/register")} {
    HTTP::redirect "https://[HTTP::host]:4443/"
  }
}

Then on port 4443 setup a virtual server with 2way SSL to the same backend pool.