Table sship_shippings_order (or sc_sship_shippings_order) is not part of AliDropship plugin or WooCommerce as far as I can see as I don't have it in my databases. So it looks like a different plugin is causing the issue.
Try disabling the plugins one by one to see which is causing the issue (starting with any plugins related to shipping) and when you find the one causing the problem contact the author.
It looks like it's only an issue when searching for an order? In which case just scroll through them manually for the time being. It isn't a database issue otherwise your site would not work at all, this is an issue with a specific plugin, causing your search field to reference a table that doesn't exist or has been renamed/removed.