Given the relative speeds, unless the IJN are caught with USN ships in engagement range before they're noticed, it seems fairly unlikely the USN will managed to get in gun range of the carriers.
One possible scenario is that the USN's learned the IJN has despatched it's fleet near to Pearl Harbour. This isn't a clear DoW but it's also very clearly not friendly and they can't chance it so Kimmel sends Kidd to sea and Short has his defenses ready and such of his aircraft as are suited for it prepared to support the navy if called on - preferably with an hour or two of notice.
When the USN learned of the IJN approach and when the IJN learns the USN has put to sea are variables. In this scenario let's say the first is determined by interception and decryption of Japanese radio traffic by a west pacific US base on 5 or early 6 December reported to Pearl Harbour and leading to the USN ships (excluding the drydocked USS Pennsylvania) putting out on 6 September and the two carriers being recalled to join them west of Hawaii (the carriers won't arrive in time to be a factor). The IJN are not aware of this initially.
The IJN aircraft are picked up on radio and a patrol of P-40s is sent up from Wheeler Field to identify them. The patrol confirm these are Japanese bombers (B5N 'Kates') and since they're in US airspace and armed, the P-40s engage causing light losses and some disruption. Wheeler Field and other air fields start scrambling the fighters they can immediately, which isn't all of them but much better than OTL.
The first wave of bombers reach Pearl Harbour and report the absence of major warships. They drop their ordnance on whatever targets of opportunity they can see (USS Pennsylvania draws a lot of bombs but since it's in drydock it can't exactly be sunk despite the damage) and do their best to escape although they're now recipients of the attention of all available US aircraft. The airfields are caught launching their available aircraft as fast as possible, making them the focus of the initial defending aircraft.
Word reaches the USN of where the IJN aircraft came from - at least approximately - and they head in the necessary direction.
The IJN are alerted to the USN's absence. While the Second Wave of aircraft are sent in to do as much damage to the naval facilities and the airfields of Oahu as possible (the IJN would rather not have to battle land-based aircraft) this is clearly the last wave for that purpose and scout aircraft are sent out to try to locate the USN warships.
With more and more US aircraft in the air and not vulnerable on the ground, losses to the Second Wave aren't as severe as the those earlier in the day. Out of date fighters trying to take on Zeros take terrible losses though.
Meanwhile, using radar to track incoming and departing fighters, General Shorts HQ has more or less localised the IJN carriers and pass this to the USN at sea who were already heading in the right general direction. The IJN, for their part, are heading west and still searching.
IJN scout planes report the USN's location while the battleships and cruisers are still a good 100 miles from the carriers. Shortly thereafter B-17s from Pearl Harbour locate the IJN's location and bomb them (to no effect).
The IJN have had time to recover and rearm their aircraft from the first wave. They now launch an attack on the USN with 70 bombers (1/3 Kates with torpedos, 1/3 Kates with bombs, 1/3 Vals with bombs) escorted by 30 Zeros. The relative handful of US aircraft from Pearl that can be used to defend the fleet are sent to intercept - predominantly USMC and USN Wildcats. This isn't sufficient to break past the escorts in any substantial number and little damage is done to the attack force.
The 70 bombers engage the 7 Battleships and 8 Cruisers, taking AA fire from the ships and from the escorting destroyers. The Kates' bombs score very few hits although the Val's bombs are more accurate, in particular to the USS Nevada and USS Arizona (where a hit to the bridge kills Admiral Kidd). The Kates' torpedoes are the big winners though: USS Oklahoma and USS West Virgina, USS Helena and USS Raleigh all suffering multiple hits. Oklahoma, the worst hit, capsized with heavy loss of life and the two cruisers were abandoned when the same seemed likely to follow.
The IJN were now moving directly away from the USN and reports indicated there was no chance of catching up with them by the remaining USN battleships. Kimmel ordered the USN to close on Oahu so they could receive better air cover and survive to fight another day. An attempt was made to engage the departing IJN with a scratch air group from Oahu but this proved unsuccessful and many US aircraft and crews were lost in the attempt. This was, however, sufficient to convince the IJN leadership they had accomplished all they reasonably could and they withdrew.
" I can't see anyone not believing that.