Powershell – Adminstrator receives PermissionDenied when issuing get-childitem in PowerShell

Short answer is no. In order for the user to interact with their data they need to use programs (bash, ls, cat, vi....). In order to use these programs the user must be able to list the directories they are contained within and read from the files which contain the programs.

You can prevent users from accessing other users data files by settings the permissions (and permissions mask) appropriately and/or restricting the access via chroot (but they can still see the config and executable files they have access to).

Ultimate goal is to prevent them from seeing system internals in File/Open

This is somewhat meaningless as an Ultimate goal - what is the threat model? How could they gain / subvert the security by doing so?

If the software supports UNC paths, you can just use those. You can also add them in Network Places via Group Policy User Configuration \ Preferences \ Shortcuts.

Alternatively, you could have the user start the software via a PowerShell script which does the appropriate actions and/or sanity checking before starting the software.