A variant of your substring transformation can do it pretty nicely:

#!/usr/bin/perl
use warnings;
use strict;

my %hash = (
            '.111' => 'Aaaa',
            '.222' => 'Bbbb',
            '.333' => 'Cccc'
           );

my %newhash = map { substr ($_, 2) => $hash{$_} } keys %hash;

for ( keys %newhash ) {
    print "$_ => ", $newhash{$_}, "\n";
}
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The output is:

C:\Code>perl newkeys.pl
22 => Bbbb
11 => Aaaa
33 => Cccc
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Update: For an in-place transformation, replace %newhash with %hash. e.g.

%hash = map { substr ($_, 2) => $hash{$_} } keys %hash;
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