sub returns a code reference on its own, no need to add a backslash. You have to add parameters to the subs, though. The canonical ones for sort are $a and $b. Localize them to the value to be sorted on so that the code still returns the full record.

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

my $sort = 'hours'; # really comes from a switch

my %map = ( #     sorting map
    hours => [0, sub {$a <=> $b}],
    code  => [1, sub {$a cmp $b}],
    name  => [2, sub {$a cmp $b}],
);

# example data
my @records = (
   [10, 'xyz232', 'secret project'],
   [ 5, 'foo123', 'world domination'],
   [ 7, 'bar666', 'have a beer'],
);


for ( sort {
               local ($a, $b) = map $_->[$map{$sort}->[0]], $a, $b;
               $map{$sort}[1]->();
           } @records
    ) {
    print "@$_\n";
}
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