But as the installation of IIS is not required and necessary its not possible to perform that via the IIS management console. You also found no options in the Remote Access Management console. So how can you change the certificate?
The solution here is using powershell.
1.) Import at first the certificate (with public key) via MMC.
2.) Once done you need the Thumbprint, you can get that via MMC or more easier via:
dir Cert:\LocalMachine\My | fl
dir Cert:\LocalMachine\My | select Subject,NotBefore,Thumbprint
3.) Once you have the certificate thumbprint you can fetch up the ID from the web application you wish to change
4.) After that you can use the ID and the Certificate Thumbprint to change the configured SSL certificate
5.) Validate the change now via:
netsh http show ssl
You can also use external services like https://www.sslshopper.com/ssl-checker.html or https://www.ssllabs.com/ssltest/analyze.html