Adding additional protections to a PSU (Meanwell IRM-01-5)
Meanwell produces good quality products (I use them regularly), so additional protections of the type you describe should not be necessary.

But the point has come up in the comments regarding your large LED bulb, and the fact that you want a "toggle" action on the button. The easiest way to do that is to get a pushbutton switch that has the required mechanical action. But if you only have a momentary switch, you can build an electronic circuit to toggle the relay. In fact, you could use a second 555 to do it.