What type of desktops are you using? Since you mention Composer I'm assuming linked clones but are they persistent or non-persistent? vCenter for Windows has been deprecated so this might be a good time to migrate to a new VCSA based vCenter.
The process to replace the SQL, Composer and Connection Servers for OS upgrades is a common issues that is well documented. For the Connection Servers you just add new replica and then decommission the old ones. For Composer you will want to follow the product documentation as there are a few extra steps.
Bear in mind that re-pointing Connection Servers to a new VC is not supported (but there is an unofficial way to do it out on the web). I've made this mistake in the past, and had a very very painful night sorting it out.
For the existing connection servers, you'd want to add the second VC separately, rather than editing the existing connection. You'd then have to recreate the pools using the new VC.
Thanks for the response. I came to this same conclusion today. I was trying to avoid it to save work but I'm seeing that there's no safe way around it, I'll be recreating the pools. Thankfully I'm not dealing with a high number of users.