Is it possible to sort .. hash ... without using any additional, supplementary arrays?

It depends what you want to do with the sorted data?

A hash table cannot he sorted directly, they have no ordering. All you can do is sort the keys.

For a single level hash, if all you want to do with the sorted results is print them out, then you can do that without storing the sorted keys anywhere (other than in the list returned by sort). But if need to remember the sorted ordering, you have to assign the ordered keys somewhere. Typically to an array.

For your multi-level hash, you want to sort the keys of several sub-hashes together, which complicates things. First you need to get all the keys of the subhashes together so they can be sorted. Then you need to obtain the values associated with those keys, and that means remembering which sub-hash each key belongs to. It may (almost certainly is) possible to do this in one pass without creating a temporary array, but it would most likely be horribly complicated and not very efficient.

It sometimes makes sense to live with complication for efficiency; or a lack of efficiency for the sake of clarity. It never makes sense to use a complicated and inefficient route just to save a temporary array.

Assuming a reasonably small hash, I'd do it this way:

{
    my @keys   = map{ keys %$_ } values %channel_db_files;;
    my @values = map{ values %$_ } values %channel_db_files;;
    my @order  = sort{ $keys[ $a ] <=> $keys[ $b ] } 0 .. $#keys;;
    print "$keys[ $_ ]\t$values[ $_ ]" for @order;;
}
00001   /foo/oradata/bar/system01.dbf
00002   /foo/oradata/bar/undotbs01.dbf
00003   /foo/oradata/bar/tools01.dbf
00004   /foo/oradata/bar/foodb-data02.dbf
00005   /foo/oradata/bar/xml01.dbf
00006   /foo/oradata/bar/foodb-index11.dbf
00007   /foo/oradata/bar/undotbs02.dbf
00008   /foo/oradata/bar/foodb-data01.dbf
00009   /foo/oradata/bar/foodb-index01.dbf
00010   /foo/oradata/bar/foodb-lob01.dbf
[download]

By the time you exit the block, the temporaries will have gone away anyway, and it will likely be both easier to read and more efficient than any mechanism that avoids temporaries.