Hi,
Why not just upgrade your joomla 1.5 website to joomla 1.7 ? Then, there is nothing to do on Hikashop's end as it's compatible with both.
Otherwise, it's a normal move of HikaShop from one website to another, which means:
install hikashop on the new website
delete the hikashop tables from the database of the new website
export the hikashop tables from the old website and import them on the new website
copy the files of the folder media/com_hikashop from the old website to the new one.
if you customized some of the views of HikaShop, you will also have to copy the folder templates/YOUR_TEMPLATE/html/com_hikashop.