UNTESTED rewrite of the first part of your code:

#!/usr/bin/perl

use strict;
use warnings;
# $ENV{PATH} = qq(/usr/sbin:/usr/bin); ?? This makes no sense - it is 
+unused

my %dg;

    while (qx|vxdg list|) {
        next if /name/i;
        $dg { +(split)[0] } = {}; 
    }


#my (@hdisks,@sizes,@nodupHdisks,@nodupLuns,@lunid,$svc,$dg,$hdisk,@fs
+,$lun);
# Process df -k ------------
    for  my $dfline ( qx|df -k| ) {
       $dg{ $_} {FS} = +(split $dfline)[6]
           if $dfline=~/$_/
              for keys %df;  
    } 


   for my $dgname (keys %dg){
     for my $vxp ( qx|vxprint -thvm -g $dgname |) {
        $dg{$dgname}{whatever} = value ...
   ....
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This way, you build up the structure %df, and don't execute the same connand repeatedly.

Also , uses qx (backtick equivalent) instead of piped open of command lines.