Thanks for all the tips!
I already tried taking a backup of the Joomla 1.5 website, upgrading it to Joomla 2.5 using jupgrade and installing the latest version of Hikashop on that. Importing the tables (_users, _user_notes, _user_profiles, _user_usergroup_map, _hikashop_user, _hikashop_order, _hikashop_order_product and _hikashop_address) from this Joomla 2.5 installation info my new website still gave me only error messages.
I read online that the extension for migrating users that you recommended (userport) would change the id numbers for my users, which would destroy the link between the Joomla user data and the data stored in the Hikashop tables. So I went looking for another solution.
I ended up taking the approach described
here
. And after importing the Joomla users I manually imported the data from the hikashop tables from my joomla 1.5 hikashop installation directly into the Joomla 2.5 database, in a similar way as described in this article. Which took some time to do table by table, but after a day of frustration finally solved my issue.
I thought I'd post how I managed to solve this because maybe someone else will benefit from these tips.
Kind regards,
Chris