The ideal situation for that scenario is that your module takes some sort of config file with the DSN for the databse connection so that you can ship it with a tailor-made config file for each of your customers.
Look at something like Config::General
to handle such a config.
Alternatively, you could make the DSN an argument that needs to be supplied by the user when running this script.
If you have a lot of stuff to do with that database then it would also be worth exploring something like DBIx::Class
to handle your database in a much more abstract way.