Krugman is not a good enemy to have, as once he has decided and pronounced on something, he greatly resents anyone presenting him with evidence that he is wrong, however compelling it may be.
Agenda cites the case of Latvia, which dared to disprove some of the great man's theories by staging a fast recovery after administering extreme austerity, causing him to pour contempt on that proudly independent small country at every opportunity. The right-wing Scots historian Niall Ferguson has also crossed swords with him in spectacular style.
Our advice to John Swinney et al is just to let Krugman's criticisms stick to the wall. Arguing with him, in however scholarly a fashion, will just make it worse.