You can change your code to:

use strict;
use warnings;
sub version {
    print "Beginning perl's \"Hello, World.\" version 2.0\n";
    }
    my $option = shift;
    $option or $option = "";
    version if $option eq "-v" or $option eq "--version";
    print "Hello, World.\n";
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This eliminates the uninitialized value error. However, you still get "Hello, World" even with an option; I'm not sure if that's what you want...
Getopt is likely the way to go (much more flexibility.)
chas