Losing two of the big fleet carriers, despite their age was regrettable, but not a critical factor in the problems facing the RN in the lead up and early stages of the war. Having a 1st line naval fighter from our perspective might look attractive as an option, and later on as the RN FAA began to change, the availability of aircraft like the sea hurricane did become vital, but in the early years of the war would have been a waste of resources and likely to lead to dangerous conclusions about the FAA needed to do to survive.
The number one problem facing the FAA in 1939 through to the end of 1940 (at least) was the supply of pilots and aircrew. The RN entered the war with at sea billets on its carriers (disregarding seaplanes), for 245 aircraft, but entered the war with just over 100 pilots. In 1939 several of the carriers, like GLORIOUS had been laid up in reserve for this reason. ARK ROYAL went to war with less than half her complement of available aircraft/pilots.
Moreover the supply of trained aircrew remained at a trickle until well into 1941. In 1939, the RN received a total of 16 trained pilots for the entire year. In 1940, 81 pilots were to receive their carrier wings (however a number of these were promptly seconded to the RAF at least for the duration of .the BoB others, despite the shortages at sea remained land based because of the dire situation in places like the western desert) In 1941, wastage overtook the supply rate. It was this cruel reality of insufficient pilots that dictated more than anything that the RN absolutely could not afford to start getting in the ring with land based air and duke it out with it in the same style as the USN or IJN. In these circumstances, the addition of a true day fighter to the inventory would have been counterproductive for a number of reasons.
The RN had no choice but to accept multi-role aircraft so that 1 pilot could do mere than one job. It wasn't shortages of deck space that forced the RN into the arena of multi role aircraft, it was pilots.
I should mention that the general conduct of the war forced the RN into situations it had sought to avoid in its pre-war planning. Prewar, it had been planned not to place its carriers within striking distance of land based air. But the invasion of Norway and the entry of Italy, as well as the surrender of the French, as well as the very late decision to hold Malta, and a bit later to lend assistance to Greece forced the RN to improvise and devise strategies and procedures that would allow them to operate in these narrow seas with some level of safety and not lose either its remaining carriers or the dwindling suppy of pilots to fly on them. Moreover, the RN in 1940 after the fall of france was in a difficult situation and had to do something to rein in the technological advantages enjoyed by ships like the RM fast battleships, and the KM heavy forces. The RN by December 1940 had received (fully worked up) just one fast battleship, and 1 carrier. They had lost 1 old BB, and two carriers, with 3 others out of theatre chasing surface raiders. They had a whole additional TO to fight against an enemy thought to have at least 3000 first line aircraft 9in reality it was more like 1700 but the british did not know that at the time.
The RN improvised. From the early part of the war, even before Norway, they had begun to train their aircrew for night operations. This took a long time, even for fully trained aircrew it would take more than a year to complete night training. Technologically they worked on night combat procedures, such as designating one aircraft as the pathfinder/ flare dropper, later on efforts were made to install an effect ASV radar (did not really come to fruition until the back half of 1941). They stretched the effectiveness of their very limited daytime fighter resources by developing GCI and radar guided interceptions for their CAP to a degree ubnknown in other navies. The RN was a much more thoroughly trained night strike force than either of the other two carrier equipped navies and this alternate strategy paid off very well, with the destruction of more than 250000 tons of shipping by the carriers alone in the med, as well as the destruction inflicted on the RM at Taranto and the KM in Denmark Strait. In those situations where daytime intervention by RN carriers was deemed necessary, such as the Malta convoys, for the first six months the RN was careful to fly air cover from out of range of the RA fighters. It got careless and overconfident in this regard resulting in the near disaster on 10 january '41.
The addition of a Sea hurricane type fighter was utterly counterproductive to the development of those abilities and ignores the fundamental weaknesses and chanllenges facing the FAA in the lead up to war. If the RN had decided to build a real day fighter force into its carrier borne assets it probably would have lost the early battles, with potentially war changing effects.
The RN leadership made the right decision not to seek to develop or acquire dedicated single seat fighters pre-war.