I know you asked about backticks, but an alternative would be to use IPC::Open3, then you could specify whatever shell you want to run your script.

#!/usr/bin/perl
use warnings;
use strict;
use IPC::Open3;

$|=1;

#my $pid=open3(\*IN,\*OUT,\*ERR,'/bin/bash'); 
my $pid=open3(\*IN,\*OUT,0,'/bin/bash');
# set \*ERR to 0 to send STDERR to STDOUT 

my $cmd = 'date';
#send cmd to bash 
print IN "$cmd\n";

#getresult 
my $result = <OUT>;
print $result;
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