The Shiden would have been a match for the Hellcat or the marks of the Seafire that saw service during the war, but it wouldn't have been able to handle a -4 Corsair.
Can't out run it. Can't out dive-it. Can't out climb it. So the Corsair can disengage at will. The Shiden lost all power at altitude so the Corsair is clearly superior there. And by the time the Shiden was in service the American pilots had learned to use speed, diving, and climbing rather than trying to turn with Japanese fighters.
To the best of my knowledge, the Shiden never carried 30mm cannons. I know it carried 4 20mm guns. And you still have the problem of being able to bring those guns to bear. The smart pilot in the Corsair can use his plane to determine when and where combat will occur and that is a HUGE advantage.
the Corsair, especially the -4, was faster, better climb, better dive, better fighter bomber, and better at just about everything once you got above 20,000ft or so.