They're anti-aircraft missiles, I don't know that a nuke could be strapped on to one of them.
But to be fair I don't know that they CAN'T strap a nuke to it.
There's remarkably little explosive in them. Most of it is fuel and guidance and some robotics in a fragmentation shell. It's more about the accuracy and efficiency of a delivery system. You could win a war with a cherry bomb as long as you somehow were able to deliver it accurately into the eyes ocket of the opposing general from your lawn.