Hi,
Yes. I would recommend to export all the tables with hikashop_ in them via your PHPMyAdmin. Then, import that on your new website's database with PHPMyAdmin, and then install HikaShop there.
Also, copy the files/folders in images/com_hikashop/upload/ and media/com_hikashop/upload/ (or the folders you configured under the "files" section of the Hikashop configuration ) via FTP from the old to the new website.
All that will be left is to reconfigure your modules and menu items to link to HikaShop's content on your new website.