Please wrap code in <code> tags - see Writeup Formatting Tips. Because you did not wrap your code in code tags, many of your [ ] pairs indicating array indices were linkified.

I understand not being able to post the vast majority of a given code, but demonstration code and pseudo-code tends to be worth 1k words.

I'm a little confused by your data structure. You wrote $base{"xx"}[0]{"ls"} (HoAoH) without specifying its value, but it sounds more like you have $base{"xx"}[0] = "ls" (HoA) from your description. For the sake of this discussion, I will sort of split the difference and assume something like $base{"xx"}[0]{"ls"} = "ls xx" (HoAoH).

If you are committed to having an array named @xx, then you need to introduce the new variables you say you are trying to avoid. However, a more natural solution (and fairly close to how I construe your last comment) would be to store the a second hash of arrays (HoA). Something like

#!/usr/bin/perl
use strict;
use warnings;
use Data::Dumper;

my %base = (xx => [{ls => 'ls xx 2>&1'},
                   {ps => 'ps xx 2>&1'},
                   ],
            yy => [{top    => 'top yy 2>&1'},
                   {finger => 'finger yy 2>&1'},
                   ],
            );

my %output;
for my $key (keys %base) {
    for my $element (@{$base{$key}}) {
        my $inner_key = (keys %$element)[0];
        my $command = (values %$element)[0];
        my $result = `$command`;
        push @{$output{$key}}, $result;
    }
}

print Dumper \%output;
[download]

This should at least give you an idea of how to avoid your naming issue. If anything is unclear, I'll be happy to clarify.