Relativistic Doomsday Device I

When I was a student studying relativity, we encountered a rather diabolical thought experiment:

A doomsday device is attached to a detonator switch. The switch has a cross section shown in the diagram below:

When the T shaped cap is placed on the U shaped cup, the button can never be pushed, since $D < L$ . Thus, the switch is always safe.

The exotic material is very strong and does not break easily, but is like any ordinary matter subject to thermal expansion, stress/strain relationship etc.

Suppose the T shaped cap is moving at relativistic speeds as it heads towards the U shaped cup. Surely in the reference frame of the T shaped cap the U shaped cup will contract in length. Thus, the button will surely be pressed!

Of course, those of us watching the U shaped cup at rest will argue the T shaped cap will contract, and $D$ becomes $D' <D < L$ .

So the world is safe . . . or is it?