I have a very old version of this module (before it was even on CPAN), and I just upgraded to the one on CPAN. It looks like there is no way to provide an MWSAuthToken for a request. Previously, it was included when creating the object.
You can pass in arguments to a method, like RequestReport:
# $MWSAuthToken is not used
$mws->RequestReport(ReportType => $report_type, MWSAuthToken => $MWSAuthToken)
But they are only used if they are specified in the parameters defined for the API call in define_api_method:
https://github.com/interchange/Amazon-MWS/blob/master/lib/Amazon/MWS/Routines.pm#L43