As an admin, I cannot schedule for a user account a Task Scheduler for an UAC program
AFAIK what you want to do is not possible with task scheduler alone. If you run as a User that is not Admin you can't run with Admin privileges and not get the UAC Prompt.
What might be possible is to create a script that uses a secure-string in an encrypted file to get admin credentials and run the script as the user but with the privileges of the saved credentials. However I don't know how "safe" this is if high security is important in your case...
EDIT: If you want to try that this might be useful.