It is possible to argue that Henry IV in this history play shows himself as politically skillful in the way that he responds to potentially dangerous and threatening situations in the present. He is determined to be a good ruler and to keep the peace in England, and this is demonstrated in his choosing to put to one side his other aims and goals as king. This is seen most clearly in Act I scene 1, when Henry opens with a speech that makes clear his own personal feelings of guilt at having usurped the crown. He desires to send English soldiers to fight in the Crusade to make amends for his sin, however, more pressing situations in England force him to delay this, as he has to deal with an uprising against the Welsh and impertinence from the Percy family, particularly in the way that Hotspur has snubbed him through keeping the majority of the prisoners he recently captured for himself. Note Henry's response to this potentially dangerous situation:
But I have sent for him to answer this;
And for this cause awhile we must neglect
Our holy purpose to Jerusalem.
Henry shows the ability to put to one side his own desires for the good of the country and for the stability of England which demonstrates his politically skillful nature. He will not let such a challenge to his authority go unanswered and determines to face Hotspur directly, showing himself responsive and flexible to situations as they arise rather than being fixed to a specific plan or goal that can potentially cause more problems in the long run for England.
Of course, it is also important to be aware that it is possible to argue the opposite. Henry, in certain places, shows himself not to be politically skillful, but rather politically insecure. As he is well aware of the way in which he seized the crown, at various points in the play he relies on his authority alone to command obedience rather than adopting more politic measures. Consider the way he commands obedience from Worcester and Hotspur on the basis of his position alone.