Can a Cold War strategy defeat militant Islam?

In ‘Foreign Affairs’ magazine, an article appeared that endorsed a Cold War strategy to defeat militant Islam. The argument was made that the war of ideology can be won without direct confrontation. After all, the Soviet Union was ideologically opposed to that of the United States, and we were able to prevail without waging active warfare directly against them. This is a great idea! We do not have to wage warfare and lose our brave young soldiers. Not to mention the wasteful expense inherent in all active warfare.
The other side of this argument is that ALL wars have differences. Many times, these differences are significant. Just two of the differences between the Soviet Union and militant Islam:

1) Militant Islam is not going for the 3rd party solution. The Soviet Union and the United States fought wars on the side. Korea, Vietnam and Afghanistan are the most obvious examples. Neither side was interested in a direct confrontation. Islam has no difficulty with the direct assault.

2) The Soviet Union was not interested in suicide. In the missile crisis in 1962, it was the Soviet Union who turned their ships around, thereby avoiding a direct confrontation (Potential nuclear war) with the United States. Repeated suicide attack is being seen for only the 2nd time of all of recorded history. It is originating from areas where Islam is prevalent. Japan resorted to suicide attack when its military situation became desperate. The ideological war has reached critical areas of Muslim control. The ‘core’ area of Islam is in the Arab lands of the Pershing Gulf. Saudi Arabia is at the epicenter.

This view sees these differences as making a ‘hot’ war not only inevitable, but also necessary. A Cold War strategy in this situation would be as effective as the non-violent containment strategy was against Tojo and Hitler. To put it crudely: It can be difficult to be non-violent when someone is shooting a machine gun at you. Nor is it wise, particularly if you have the means to shoot back.