Hi,
You could export/import the tables: hikashop_order, hikashop_order_product, hikashop_address, hikashop_history and hikashop_user.
You'll have to use the "check database" button of the HikaShop configuration to add the new columns in these tables after you migrate them to the new website.
Note however that for the user accounts in Joomla, it's the table users, but if the version of Joomla is not the same, you might have some issue with that that you'll have to deal with. If you don't migrate the users table, the orders will be seen as made in "guest" mode and the new users won't be able to use their user account.