Hi,
Is the step by step to migrate to Joomla 1.7:
If you want to migrate HikaShop, you need to install it on your new website (you need to have the same version than the one installed actually on the previous website). Then, you need to go to phpmyadmin and delete all the jos_hikashop_ tables from the new website and then export the tables from the old website and import them on the new website. Then, via FTP, you need to transfer the content of the folder media/com_hikashop to the new website, the content of the folder templates/YOUR_TEMPLATE/html/com_hikashop (if you modified some of the views) to your new website, and finally the languages/en-GB/override content (if you have some override translations) to the new website.
So yes, you should copy the hikashop tables from your old website to your new website database. Note that if you're not using the same table prefix from both websites, you will have to change the name of the tables after the import if you want HikaShop to pick them up.
The modules and menus you have for hikashop will have to be created again on joomla 1.7