Upstream Pi-hole DNS servers are universally used by all connect clients using that Pi-hole. There is no ability to assign different upstream DNS servers to different clients in a single Pi-hole instance.
To accomplish your goal, you would need a second instance of Pi-hole that uses the desired upstream DNS server for the clients using that Pi-hole.
Or, if I don't fully understand your question, and the question is different:
You do have an option to assign a different DNS server to clients during the DHCP handshake. This would put those clients on a DNS server other than Pi-hole.