Royal Navy
To be honest I think being allowed to build 15,000 ton carriers in unlimited numbers between 1922 and 1937 would have nil effect on the Royal Navy.
IOTL the RN produced the 10-year modernisation plan that I often refer to. Under that plan the RN was going to keep Courageous, Glorious and Furious which between them absorbed 66,000 tons of the 135,000 tons allowed under the 1922 Treaty. The remaining 69,000 tons would be absorbed by four 17,000 ton carriers to be ordered in 1924, 1928, 1931 and 1934 for completion in 1928, 1932, 1935 and 1938. Of these only the 1934 Carrier, the 22,000 ton Ark Royal was actually built. The 1924 plan also included 3 or 4 smaller carriers displacing less than 10,000 tons for trade protection and these weren't built either.
ITTL I think the RN would instead plan to build three 23,000 ton carriers with the remaining 69,000 tons because 17,000 ton ships would not be significantly better than unregulated 15,000 ton ships. However, only one would be built and that would be a 23,000 ton version of Ark Royal. If it was up to me I would have used the extra 1,000 tons to fit better lifts and if anything was left after that increase the width of her hangars from 60 to 62 feet.
Under the above plan Eagle would have been scrapped or converted to an auxiliary. However, Argus and Hermes would have been retained as trade protection ships because they displaced less than 15,000 tons. As the requirement was for 3 or 4 trade protection ships a 15,000 ton ship would be designed, but it would not be built because the Treasury, Parliament and Great British Public would not put up the money.
When the purse strings were loosened in the middle 1930s and the tonnage quotas abolished the RN initially planned a mixed carrier force of 23,000 ton fleet carriers and trade protection ships of about 15,000 tons. However, the estimated costs were £4 million for the Illustrious class and £3 million for the trade protection ship, which was not considered satisfactory. As the Illustrious cost only one million Pounds more and was a satisfactory design (among other things it could carry 36 aircraft vs 18 in the smaller ship) it was decided to only build the larger ships.