You are right that classic fascisms tended to appear as corruptions of a democratic process in which a population had at least partially lost faith. True in Italy and Germany, and in a different way, in Argentina. Not true in Spain or Chile, where fascist regimes took power without an electoral mandate, but did use "managed" elections to legitimize themselves later.
I doubt that fascism is "specifically Western." Japan from 1928 to 1945, Taiwan under Chiang, and Burma today might all qualify as "fascist." The signature feature of fascism is regimentation of society around a "national salvation" theme. It will always claim to be a popular mandate even when it is not, because its legitimacy does not rest on constitutional, or any specifically political, processes. Its legitimacy (in its own eyes) rests on its supposed unique ability to express the will of the nation.
"Islamofascism" seems to me to fail on two counts. One, it is not national. Two, it bases its legitimacy not on the will of the nation, or the people, but on the will of God. Classic fascisms have usually been willing to ally with religion (Mexico was a notable exception; the Burmese generals have tried to co-opt religion but apparently have not been successful), but have never, to my knowledge, claimed a specifically theological basis.
However, Islam might be a special case where religion is concerned. Fascisms have tended to distrust religion because they think it divides the people's loyalty and inculcates undesirable attitudes, e.g., ethics, compassion, etc. Islam, which has never recognized a clear distinction between the religious and the secular, and which is a notably militant creed, might meld better with the fascist style than other religions.