One trick that I've used in the past is to modify @INC to also point to a directory I can modify (e.g. lib in my software release) and then require the module:

my $dir = Cwd::getcwd() . "/" . $0;
$dir =~ s#([/\\])[^/\\]+$#/lib#;
push(@INC,$dir);

require PrivateModule;
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That way you are only affecting your own script and you can use the standard module.