You can't effectively deny rights to local administrators, since regardless of what GPO you apply, they can always override it at least temporarily by editing the registry. They can also remove the computer from the domain.
In general, you shouldn't use or distribute the local administrator accounts in an environment requiring top-down administrative control such as this. The best policy is to keep those passwords within a database (or software designed for this purpose such as Hitachi ID Privileged Access Manager, which I used to work on); the passwords should only be used when necessary to re-establish the domain relationship or similar, and use of them should be auditable.
It's unfortunate that your application requires such access. You could consider determining what access it actually requires, and giving it that instead; most applications do not actually need administrator access.
If your only goal is to prevent inadvertent shutdowns, you can certainly set
Local Security Policy/Local Policies/User Rights Assignment/Shut Down the System to exclude them, but be aware that this will not prevent a knowledgeable user from intentionally shutting it down. I believe this policy applies to RDP interactive sessions, but not to the
shutdown command (which has an option to target a remote host); that is the domain of the
Force shutdown from a remote system GPO option.