Hi,
You can use the mass action system for that:
You can for example create a mass action like that to delete all the customers without a confirmed order :
monosnap.com/file/JhFLXjNCpnxc9rAKKuUUNG7i5E5nyA
There is no way to set a "more than 1 month old" condition there though.
Actually, if you don't set any filter, it will delete only the users without an order as HikaShop will refuse to delete users with orders. The orders would have to be deleted first.
And note that while this will delete the "customer" entry in HikaShop, it won't delete the user account in Joomla (but "guest" users will be completely removed).
If you want to do it in MySQL and supposing that you want to delete the user accounts from Joomla, you'll have to have a DELETE query on the joomla users table with joins to the hikashop_user table on the users.id = hikashop_user.user_cms_id and on the hikashop_order table on the hikashop_user.user_id = hikashop_order.order_user_id, and a condition on hikashop_order.order_status if you want to take into account only non confirmed OR shipped orders, and a condition on hikashop_order.order_created if you want to have a "only less than 1 month old orders" condition.