Replacing LTMs in GTM Server List

The method is correct, however you can't proceed without loosing virtual servers because they exist within the server you want to delete. So in case you can't use virtual servers auto discovery, you have to create them again. I suggest you export them before deleting the server using:

tmsh list gtm server YOURSERVER virtual-servers one-line

Keep the output in notepad. And after adding the new server (I assume with the same name), add the lines using:

tmsh load sys config from-terminal merge

Regarding pools, you will not loose them, however I'm pretty sure you have to remove from them any references to the virtual servers you need to remove