Hi GavS,
Welcome to Community! QuickBooks Online currently doesn't have an option to assign classes with the batch actions tool. However, with QuickBooks Online Accountant and QuickBooks Online Advanced, you can reclassify multiple transactions at once. I suggest reaching out to your accountant for assistance. If you don't have one, we can help you locate a ProAdvisor in your local area.
If you have any other questions, please don't hesitate to reach back out. We'd be happy to help!