Fascism as an ideology wasn't all that viable by the time of the Cold War. It involved a style of mass politics that had to be tied up in revanchism and the social realities that existed before WW2. The era of superpowers wasn't going to allow that to continue. The closest to Fascism after WW2 (in Argentina and Ba'athist Iraq) were not really active or independent Cold War actors.
It would have to be a bloc of traditionalists and reactionaries. Think Portugal, Francoist Spain, South Africa, Rhodesia, Taiwan post-Nixon, Marcos ruled Phillipines, Junta ruled Brazil and Junta ruled Argentina, perhaps Malawi.
Maybe in an Alt History example, an independent Pied Noir dominated Algeria (or maybe just an enclave in Oran and Algiers), as well as an independent Katanga, or a longer lasting and more ambitious Greek Junta. I could also see, in the event of a successful Portugal, and therefore a successful Rhodesia, a sort of Finlandization of Botswana into this bloc (they'd be basically surrounded).
In a really big stretch, perhaps a more right wing France that has serious disagreements with the US that go beyond de Gaulle's ego and posturing at Great Power status.
Essentially, these would be "not for polite company" quasi-allies to the West. They could be part of some alliances with the West, but would not be subservient.