I haven't quite understood what you're trying to do but

m#^(?!-\s)$#
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Will only match an empty string (which you don't have in your @ARGV as far as I can tell). And

m#^(-\s)$#
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won't match anything either because Bash removes all unquoted whitespace.

I also have no idea why you're pushing and shifting, so I don't know whether you're using them incorrectly, but my intuition says 'yes'

Anyway, Perl can do backticks and can change directories, so your users don't need to bother:

use strict;
use warnings;

sub usage {
    die <<END
Usage: $0 <directory of binaries you want to test your knowledge of>
For example:
$0 /usr/bin
END
}

my $path = shift or usage();
-r -x -d $path or usage();
chdir $path or die $!;

my @whatis;

print "wait a little...\n";

for (`whatis --wildcard * 2>/dev/null`) {
    chomp;
    push @whatis, [ split /\s+-\s+/, $_ ];
}

print "(control-d to exit)\n\n";

MAINLOOP: while (1) {
    for (@whatis) {
        print $_->[0];
        defined <STDIN> or last MAINLOOP;
        print "\t", $_->[1], "\n\n";
    }
}

print "\n";
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