I don't think this will work because of the way merge sort is implemented in Perl

It is first comparing all pairs in a breadth first search, which would mean far too many disk operations and no sensible caching option

  DB<7> sort { print "$a,$b  |"; $a <=> $b } reverse 1..16
16,15  |14,13  |12,11  |10,9  |8,7  |6,5  |4,3  |2,1  |15,13  |15,14  
+|11,9  |11,10  |13,9  |13,10  |13,11  |13,12  \
|7,5  |7,6  |3,1  |3,2  |5,1  |5,2  |5,3  |5,4  |9,1  |9,2  |9,3  |9,4
+  |9,5  |9,6  |9,7  |9,8  |
  DB<8>
[download]

explained

16,15  |14,13     |12,11  |10,9     |8,7  |6,5    |4,3  |2,1  |       
+      # sort pairs
15,13  |15,14     |11,9  |11,10                                       
+      # sort 1st and 2nd 4-tuple
|13,9  |13,10    |13,11  |13,12                                       
+      # sort 1st 8 tuple
                                    |7,5  |7,6    |3,1  |3,2          
+      # sort 3rd and 4th 4-tuple
                                    |5,1  |5,2  |5,3  |5,4            
+      # sort 2nd 8tuple

      |9,1  |9,2  |9,3  |9,4  |9,5  |9,6  |9,7  |9,8  |               
+      # sort 16 tuple
[download]

A caching/memoizing of data read from disk would be far more efficient if the chunks were strictly chosen depth first.

FWIW WP lists some divide-and-conquer approaches for merge-sort

https://en.wikipedia.org/wiki/Mergesort#Parallel_merge_sort