Given that you have ssh access to the particular server in question, I would expect that you have a home directory there with write permission, where you can store a perl script as an actual file. So why not just put your perl one-liner into a file on the remote server, and make things simple and clear in the local script:

$cmd = `ssh server perl my-remote-one-liner`;
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I couldn't tell from the OP what sort of args the remote one-liner script was expecting for @ARGV. If including those within the back-ticks for the ssh command is complicated, I would switch from using back-ticks to opening a pipeline file handle, so that I could submit the args as separate list elements (not to be interpreted by the remote shell):

{
    my @ssh_cmd = qw/ssh server perl my-remote-one-liner arg1 arg2/;
    open( my $ssh, "-|", @ssh_cmd ) or die "ssh failed: $!";
    local $/;
    $cmd = <$ssh>;
}
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Note that the curlies establish scope for the "local" use of slurp mode, and for the shell file handle (using "my" within the block limits the scope for the variable, whether or not you "use strict;" -- but you do use strict, right?