You can use the path in your call to get. Replace your call to get with this one. 
$ftpBox->get("$remotedir/$filename","$destination_dir/$filename") 
 or die "failed to get $filename to $destination_file";

[download]

If your just interested in checking to see if a directory exists. Then an ls or dir is almost as good as cd. 

$ftpBox->ls($remotedir);
#or 
$ftpBox->dir($remotedir);

[download]
Updated: Added a little more info.

In reply to Re: Net::FTP Server does not support cwd...alternatives? by atopolc
in thread Net::FTP Server does not support cwd...alternatives? by linebacker

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