Without an assignment shape to create the assignment object, there's nothing to route ... Can you provide further information, what are you trying to achieve? For example are you trying to re-assign an existing assignment to a different operator or workbasket?
If you simply want to change the assigned operator in an existing assignment, you can use a router activity, but as I said, the assignment has to exist first and also you'll need to open in the clipboard to change the AssignTo property accordingly.
Fundamentally, assignment shapes create assignment records which are assigned to operators, so you can't assign anything to an operator unless there's an assignment first. The case is not assigned to an operator, which is why we use the assignment shape to create and route tasks .. hope this helps