Hi,
The best would be to create a new development environment and duplicate the old site.
Then on this dev version, update HikaShop to the latest version, the 2.6.3, same thing for the new site, update it to the latest version. Then migrate all the HikaShop tables from the old to the new site, that way you are sure to migrate all the data and using the dev environment will not broke the production website.
You will need to have the latest data from the Joomla user table up to date too, but this is a Joomla thing