Can anyone confirm whether the installation of a new Level 6 licence from Level 4 will, in any way, affect the existing router configuration or KVM machine which we already have installed? Thanks.

You will be fine.

I suggest you read the changelogs of every new version from 4 to 6. Many changes and additions have happened drom 4 to 6.
Do it on test environment before you move to production. It will spare you of many hadakes.

Cheers