A negative look-ahead is fine, just move the .* into the assertion.

if ($s =~ /^a(?!.*ab).*b$/) {
[download]

Cheers,

JohnGG

Update: If you want "a00000000ab" to match then you could change the look-ahead to ensure there is at least one character after the "ab".

use strict;
use warnings;

my @strings = qw{
   a000000000b
   a0a0000b00b
   a0000ab000b
   a00000000ab
   };

print
   m{^a(?!.*ab.).*b$}
   ? qq{$_: matched\n}
   : qq{$_: unmatched\n}
   for @strings;
[download]

which produces

a000000000b: matched
a0a0000b00b: matched
a0000ab000b: unmatched
a00000000ab: matched
[download]