This is really going to depend on which version of the Buffalo you compare it to. The F2A-2 was reasonably fast, handy, and a quick turner. It was well liked by the pilots who flew it, including Pappy Boyington of "The Black Sheep" fame. The "improved" F2A-3 was significantly heavier due to increased fuel and ammo capacity and armor for the pilot. It was an absolute turd in a dogfight, sacrificing maneuverability to range and pilot protection.
The XP-36D model would have been the model you were looking for. It had two .50 cals in the cowling and four .30's in the wings. It would have been very comparable to the F2A-2, but would have flown rings around the -3 Buffalo. The drawback would have been it larger size, compared to the Buffalo. This becomes critical for shipboard stowage.
In the end, it would have made very little difference. Both aircraft had approximately the same performance and could be outflown by the Zero, and by a Wildcat in the hands of a good pilot. The Wildcat ultimately proved to be the better aircraft and thus the better choice for the USN/USMC.
By the way, your designation of a navalized P-36 was actually used by Curtiss for a high altitude interceptor that was developed later in the war. It was not put into production.