It is all based off of the connection string line, the rest of the code doesn't care who logged in.
This is the line you need to modify (right now it is set to integrated security):
$SqlConnection.ConnectionString = "Server = $SqlServer; Database = $SqlCatalog; Integrated Security = True"
To help you out with what to put in this line, check out this website:
http://www.connectionstrings.com/