While a hash is a bad data structure for this, a BTREE looks a lot like a hash programmatically, but this question is easy for a BTREE. Unfortunately in the most convenient BTREE implementation to use from Perl, the API is a little convoluted:

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

tie my %hash, 'DB_File', undef, O_CREAT|O_RDWR, 0666, $DB_BTREE;

%hash = (
  '1' => 'cat',
  '3' => 'mouse',
  '5' => 'whale'
);

tied(%hash)->seq(my $key = 2, my $ans, R_CURSOR);
print "Found key $key, answer $ans\n";
[download]

The main reason for this API being so complicated is that you generally want somehow to indicate both the key and value discovered. This doesn't fit with the appearance a basic hash lookup. Therefore the attempt that tie makes to turn something else into an illusion of a hash has to break down..badly.