According to SuiteAnswers, I should be able to set the Default Transfer Order Status to 'Pending Fulfilment' and this will prevent the need for approval on Transfer Orders:

I specifically want to allow 'normal' Transfer Orders to be generated without approval, but then any Transfer Orders created by the 'Replenish Location by Transfer Order' process should go for approval before Fulfilment.

This setting doesn't seem to work. I have it set (as above), but when I create a Transfer Order it shows as Pending Approval:

(And I've double checked that when saved it shows as needing approval).

I have looked to make sure there are no workflows setting this field to Pending Approval (in fact we previously has a Workflow setting it to Pending Fulfilment in order to override the Approval process).