What if the Japanese inflict more casualties on the Americans during the Battle of the Coral Sea? (by that I mean sink more of the carrier force) Would the invasion of Port Moresby go on? How would it affect the rest of the war?
If Nimitz didn't bother sending better air units to Midway with 3 carriers, he's unlikely to do so with 2 carriers.
Most direct way for Hara to sink two carriers is to connect on May 7th with his large strike to Neosho, redirected onto Fletcher.
They probably still try the invasion but as stated, with Hara's air groups badly beat up and one of his decks probably still badly damaged he is hard pressed to provide air cover to the invasion...
Nimitz probably still commits TF-16 and he may try harder to get SARA to Hawaii in time. You also have a good chunk of SARA's OTL air group sitting around in Hawaii (most of them actually went to sea with Y-TOWN for Midway). Some of them will be retained for SARA when she arrives but some may go to Midway meaning Midway has a better trained air group.