So if I don't want to go through the hassle of recreating DBMs when I copy from one computer to another, and if possible, not to worry about checking versions on all of my computers to make sure they're the same, and I don't want to hassle with using dd or cpio, what options to I have?
Make sure you are using the same format on each machine. You could use tie %hash, DB_File, 'file'; which specifies which DB type you want to use explicitly (unless you use AnyDBM_File :). Also, dbmopen has been deprecated since Perl 5.
Try compressing the data file and then transferring, or, if there's more than one, compress all of them first, and then tar them together.