How is a regular expression going to help me accept 4294967295 (UINT32_MAX) but not 4294967296 (UINT32_MAX+1)?

AnomalousMonk answered this one; I suggested the module because it's good for verifying various number formats.

I would rather avoid the overhead of using Math::BigInt if I can.

Well, if you want to go right up to that limit*, then I think the safest way is to use Math::BigInt, because it'll correctly handle strings that are clearly over the limit. It's a core module and it's not really that much overhead: once you've used the module to confirm that the number will work as a normal integer without loss of precision, you no longer need the object and can just work with a plain Perl scalar afterwards. Just an example:

use warnings;
use strict;

use feature 'state';
use Carp;
use Math::BigInt;
use Config;
use Regexp::Common qw/number/;

sub validate_int {
    my $str = shift;
    state $max = Math::BigInt->new(
        eval $Config{nv_overflows_integers_at} );
    croak "not an integer"
        unless defined $str && $str=~/\A$RE{num}{int}\z/;
    my $num = Math::BigInt->new($str);
    croak "integer to small" if $num < 0;
    croak "integer too big" if $num > $max;
    return $num->numify;
}


use Test::More;
sub exception (&) { eval { shift->(); 1 } ? undef : ($@ || die) }

is validate_int(0), 0;
is validate_int(1), 1;
is validate_int(3), 3;
ok exception { validate_int(undef) };
ok exception { validate_int("") };
ok exception { validate_int("x") };
ok exception { validate_int("123y") };
ok exception { validate_int(-1) };
ok exception { validate_int("-9999999999999999999999999999999") };

my $x = Math::BigInt->new(eval $Config{nv_overflows_integers_at})-1;
is validate_int("$x"), 0+$x->numify, "'$x' works (max-1)";
$x++;
is validate_int("$x"), 0+$x->numify, "'$x' works (max)";
$x++;
ok exception { validate_int("$x") }, "'$x' fails (max+1)";

ok exception { validate_int("999999999999999999999999999999999999") };

done_testing;
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* Update: I named several integer limits in the post I linked to. Depending on which of those limits you want to use, hippo's suggestion from here is of course much easier.