Hi,
The best solution would be to update your HikaShop version on the old website first.
Then install the new site with the newest version of HikaShop, that way on both sites HikaShop has the same tables and columns in the database.
And then export/import your database for HikaShop tables from old website to the new one.
Be careful regarding the Joomla users during the migration, their IDs must be kept during the migration else there could be some issues.
And of course, it is always a good thing to do backups and work on dev environment.