I'd be inclined to do this, which pre-codes them in the desired order:

@user_types =(
    [ '037' => 'member' ],
    [ '165' => 'public' ],
    [ '022' => 'staff' ],
    [ '683' => 'babe' ],
    [ '001' => 'old fart' ],
);
[download]

Then you can make a hash for looking up the labels by doing

%lookup = map { @$_ } @user_types;
[download]

However, if this is something that happens a lot in your code, you might consider making your hash order-remembering, e.g. by tieing it to Tie::IxHash:

use Tie::IxHash;

tie my %user_types, 'Tie::IxHash';

%user_types = (
    '037' => 'member',
    '165' => 'public',
    '022' => 'staff',
    '683' => 'babe',
    '001' => 'old fart',
);
[download]

Then accessing the hash via functions like keys, values, and each gives you the data in the desired order.