We can’t see infra-red and so if the manufacturer of your remote control hasn’t provided a LED, you won’t know if its working or not.
However just about every digital camera can see infra-red. So view the business end of your remote through your camera and you’ll see the transmitter flash in response to your button pushes.
A similar technique can be used to see if a fibre optic cable is active.
A Simple Solution from Redback