It's very easy to change up to a current FMP version. There's really nothing to it. The program converts the v.7 files to v.12 usually without incident. I would make the move to a current OS on both machines and upgrade to FMS and FMP 15.
This surprises me. I am a user with no programming experience. Someone who supports Filemaker databases as part of her job tried and it did not work properly. She quit after a couple of tries because supporting my work is not part of her job. The issues are preserving all of the functions of the database as well as the data. We have plenty of machines running current OS's.
What would a reasonable cost be to pay someone to convert the database?
You would also have to upgrade FMS.
You can search for a consultant FileMaker Consultants, Data Consultants, Database Consultants
and or contact your local Apple Store and they maybe able to refer you to a local consultant.