Can I just switch to a different type/brand of catheter? 

You can switch the type and/or brand of your catheter without any problems, as the action stays the same. The packaging or the design of the catheter can possibly differ from what you are used to but that will not cause any inconvenience, especially not if you are an experienced user. Consult the employee of your medical specialty store or pharmacist on the handling process of the health insurer.