I tried putting the Numeric.pm file by itself first, and then the full Scalar/ directory, and then tried to execute its contents using do. Didn't work.

You didn't include the DLL. These are the files installed by the distro:

• Scalar/Util/Numeric.pm (in the site lib dir)
• auto/Scalar/Util/Numeric/Numeric.so (or .dll, in the site lib arch dir)
• Scalar::Util::Numeric.3 (in the man3 dir)

You can find these files in the blib dir created during the installation process.

I don't want to require users to install anything

As a module with a compiled component, this would only be possible by providing binaries that are suitably compiled for your users. Keep in mind that modules compiled with one version of Perl are only compatible with that version of Perl. This would a large headache.