I have done a bit of searching around on this and have experimented with some code examples. In my testing I was not able to successfully capture the ctrl + v to prevent the pasting.
It seems to me that this may be possible but it would require some custom js coding to add this in. In the examples I saw you will have a special function that is called in the onkeyup or onkeydown events. This function basically checks for the control key and the v key being pressed at the same time. In most of these functions they use the following for the ctrl key:
event.modifiers & Event.CONTROL_MASK
They make reference to the v key as:
event.keyCode == 86
event.which == 86
The function I was working with set variables to these values then in an if statement just look for both of the variables together. If true it would just clear the text field.
While this may be possible to do with the code getting it implemented correctly could present a bit of a challenge if it is not something you are familiar with.