Hi,
Well, the biggest problem with migrating only HikaShop and not the whole website, is what you're going to do about the user accounts ?
If you plan on loosing them, then just export all the hikashop_ tables from your old database, import them in your new database with the correct table prefix and then install HikaShop on the new website. That will link the data with the rest. You'll also want to copy the files from images/com_hikashop and media/com_hikashop/upload/safe to the new website to keep your HikaShop images and downloads.
If you don't want to loose the user accounts, you'll have to migrate them between both websites (you'll find several extensions for Joomla to do that), and once done, you can do like explained above.
We don't have a documentation on that as there are many ways to do a HikaShop migration based on what you want. Some people don't want to migrate the orders, only the products, some want the user accounts some don't, it depends on the Joomla version of both websites etc.
But most of the cases have been talked about on this forum. For example:
www.google.com/search?q=hikashop+migrate...ikashop.com&safe=off