Solution
NI Package Manager requires administrator access due to needing to install low-level device drivers, install files to protected directories, and change Registry keys. There is no way to run NIPM without admin access.
The UAC prompt is a Windows security feature giving the user warning and requesting authorization for this level of access. To alter the behavior of the system regarding these prompts, the user would need to work with their IT to alter local group security policy, since this is not something controlled by NI.