I'd add another level of paranoia and make a backup to yet a different name because if you run this twice with a bug then you've overwritten your good backup.

Assuming you can ensure that this is good CSV format you can also attack these files as if they were SQL databases by using DBI and DBD::CSV or DBD::RAM. If the files are really long DBD::RAM may be the best because it looks like it can refrain from reading the whole file into memory. But for not so huge files the above strategy is probably fastest.

You probably want to do some tests or just monitor the output on the screen, in case you have bad data (maybe embedded commas?) which could throw off the routine.