Not sure why you're having problems with installing that module on 64-bit Perl. If you're looking for help with that, you can post more details here and ask for help from others and/or you can also submit a bug report with the module's maintainer.
If you wanted to use 32-bit Perl on 64-bit Windows, you can. You just won't be able to leverage any 64-bit features of Perl (such as 64-bit integers). Unless you really need those features, you shouldn't have a problem. In your case, it sounds like you're moving your existing script(s) from an older environment (presumably 32-bit OS & Perl), so using 32-bit Perl on 64-bit Windows won't be a problem. In my personal use, I haven't had a need for any 64-bit Perl features, so I've been sticking with 32-bit Perl even on 64-bit Windows.
As for using another module, the first obvious alternative is to use Win32API::CommPort, which Win32::SerialPort is using underneath and "provides an object-based user interface to allow higher-level use of common API call sequences for dealing with serial ports". However, I think I would prefer to stay with Win32::SerialPort myself.