Hi,
I've had success bending 1/8" copper tube by inserting a length of nylon strimmer line into the tube before bending. 1.65mm line is a snug fit. The line is removed after bending the tube using a metal plate with a 2mm hole drilled in it. The line is threaded through the hole and the end of the tube butts up against the plate. The line is grasped with a pair of pliers and levered out by pivoting the pliers against the plate. I can get tight bends with no kinking.
It's important that the line is removed after each bend is made as the resistance to being pulled out increases with each bend until it snaps off instead of coming out. Then you are up for heating the tube and applying compressed air until molten plastic is squirted across the workshop.
I'm not sure strimmer line is available in the diameter needed for 3/16" tube, but if it is, it might be worth a go.
Regards,
Alan