Just out of curiosity, why do some authors assume that once Spain joins the Axis, it would seek immediately invade, if not outright annex Portugal? The Portuguese Estado Novo under Salazar was a proto-fascist regime, to put it kindly. While not an ally of Hitler, Salazar was certainly sympathetic, and did not do much more than necessary to assist the Allies. Why take the risk to replace a neutral/leaning Axis regime? Without vastly expanded naval power, the Axis could never hope to secure Azores, and the situation in Manstein in Africa that led to the capture of the Azores was a bit fortuitous.
As for Spain, why would Franco want to take on his former backer? Franco would not have triumphed in the civil war without the assistance of Salazar, something he must have been aware of. The Estado Novo and the "Spanish State" were near ideological clones. Spain and Portugal have only a few border disputes, none of which are outstanding in Portugal's favor.
Far more likely, in my opinion, would be the Portuguese being bullied into a Pro-Axis stance rather than being invaded. It would probably cost them their African colonial empire, but given the choice between being invaded, and being (temporarily) deprived of its Empire, I think Portugal pay that price for its continued independence.