Wow, rubber duck debugging really works :)

More seriously, I will simply answer myself to maybe help someone with the same question. Openerp allows you to write migration scripts. Searching around, I just found the openerp/modules/migration.py file containing a really great description of how to do upgrade pre or post treatment.

        This class manage the migration of modules
        Migrations files must be python files containing a "migrate(cr, installed_version)" function.
        Theses files must respect a directory tree structure: A 'migrations' folder which containt a
        folder by version. Version can be 'module' version or 'server.module' version (in this case,
        the files will only be processed by this version of the server). Python file names must start
        by 'pre' or 'post' and will be executed, respectively, before and after the module initialisation
        Example:

            <moduledir>
            `-- migrations
                |-- 1.0
                |   |-- pre-update_table_x.py
                |   |-- pre-update_table_y.py
                |   |-- post-clean-data.py
                |   `-- README.txt              # not processed
                |-- 5.0.1.1                     # files in this folder will be executed only on a 5.0 server
                |   |-- pre-delete_table_z.py
                |   `-- post-clean-data.py
                `-- foo.py                      # not processed

        This similar structure is generated by the maintenance module with the migrations files get by
        the maintenance contract

In my case, I just wrote some SQL queries in order to copy data from the old table to the new one and also from old FK to new ones. After that, I also cleaned up the old fields and old table to keep the database clean.