If you, like me were looking for hours how to use the CRS here's the answer:
right-click on any hotspot to call the inventory menu, then RIGHT-click on the CRS, and it will be used on the lock picks.
Very counter-intuitive,

It would be counter-intuitive, except the game tells you how to use it right after you get it.

I must have clicked the moment I was given that message because I haven't seen it.
It happened a few times to me then when I wanted to move the character a message appeared the same time, and it was closed that way simultaneously...

I have the same problem, but without a fix.
I have read this advice both here and on Wadjet Eye Games forum, but it doesn't work.
Clicking on any hotspot brings up the inventory, but selecting the Carbon Ray Stabiliser just gives a message akin to, "I can't use that here."
I left the room before I fixed my lockpicks, and returned later, so perhaps the game is broken at this point.On a separate note, clicking through speech/messages accidentally seems to be a problem. E.g. finishing a gunfight, I ducked back for cover, but the next messages were already showing and I missed at least two of them.