Hi,
Well, it's not easy to backup only HikaShop data since HikaShop is linked with Joomla's data. For example, your orders are linked to the users in Joomla and your Hikashop menus and modules are saved in Joomla tables while the HikaShop options are stored in HikaShop tables.
So based on the data you already have in Hikashop and what you want to keep, you might need to backup joomla's stuff as well.
In short, all the data of Hikashop is stored in the hikashop files in the database. And the files uploaded for HikaShop are stored in the folder media/com_hikashop. If you have view files overrides, they are in the folder templates/your_template/html/com_hikashop
So you would have to first export all that. Then, install the same version of HikaShop on the other site and finally important all that data back in the new website.
The problem is that if you don't export/import as well the users of Joomla and that they get the same ids in the new website, the orders/addresses won't be linked to a user or not to the correct ones. You will have to redo your menus and modules.