First of all, XML::LibXML (and thus XML::LibXML::SAX) come with Strawberry Perl. So you do have the module.
In your Perl installation, there's a file named XML/SAX/ParserDetails.ini that says which SAX parsers you have installed. XML::Simple uses the first parser listed in this file. For you, that parser is XML::LibXML:SAX.
The problem is that PAR::Packer doesn't know this, so it didn't include XML::LibXML:SAX in the distributable package. You'll need to notify PAR::Packer of this when you create the distributable package.
pp -M XML::LibXML::SAX ...
Updated due to a better understanding of the question.