The issue is really about airplanes, not aircraft carriers, per se.
I don't think you could completely avoid some experimentation with the concept or airplane carriers in the 1918-1930 period by the major maritime powers (UK, US, and Japan). However, it is not beyond the realm of possibility that political pressures and prejudices in these nations could have lead to a situation where offensive airpower became centralized in Army aviation corps or in fully independent air forces. Airpower might have been seen primarily as a tactical compliment to landwarfare or as a means of strategic long-range bombing - and most of the money and research could have gone to these ends. Since heavy level bombing is pretty useless against ships at sea and, at least until the late 1940's, vast stretches of blue ocean would be outside the range of land-based tactical bombers, the primacy of the battlefleet in sea control would remain longer. Couple this with more aggressive and successful lobbying by "battleship admirals" ,I could imagine a situation where naval aviation is considered almost solely as a means of scouting and defense against specific foes such as submarines and possibly convoys. Aircraft carriers might be built, but they would be smaller and/or they would be convoy raiding or scouting hybrids like the abortive US Navy crusier/carriers of the 1930's. And yes, airplane carrying Zeppelins, might have fulfilled a lot of those roles as well. It is not out of the range of possibility that airplane carriers would have never assumed the importance they did in our TL before naval research switched to guided and ballistic missiles to provide capital ships with long range standoff offensive capability.
So here's my summary of fantasy ships of this time line, by decade, taken from alternate Janes Fighting Ships editions of 1919, 1938, 1946, 1955, 1967, and 1999.
HMS Glorious 1919-1928. Originally planned as a light battlecrusier with 2x15" and then 2x18" guns, the ship was modified in 1918 to carry 10 scouting bi-planes and a flight/handling deck aft of the superstructure, replacing the aft turret. The planned 18" inch gun forward was replaced by a new quadruple 8" turret, as it was believed the quicker firing main armamement would be more suited to thew new scouting and independent cuising role planned for this ship. It is interesting to note that early sketches for this conversion featured a full flight deck forward and configured for use by land planes as well as floatplanes. The main guns were placed aft. This design was scrapped as soon as it was presented to the Admiralty. As First Lord Jellicoe is rumored to have said, "The Royal Navy has never turned tail and run from an enemy before; I do not intend to see any ship placed in His Majesty's service which is designed to do just that!" The ship was always considered a failure and was scrapped in 1928.
USS Lexington 1929-1942. One of six battlecrusiers planned for the US Navy as the arms race among Britain, Japan, and the US heated up, Lexington was modified while still under construction to serve as the flagship and core of the experimental "1st Independent Airship Scouting Squadron" based at Pearl Harbor. Only the fore 16" turret was retained and the remainder of the ship was given over to a huge cantilevered hangar deck, a collapsable mooring mast, and retractable hangar walls capable of creating an open-topped hangar. The original 7 funnels were trunked into two huge exhausts venting over each side of the ship. The ship was intended to service three 5,000,000 cubic foot Topeka ZR-4 class scouting airships, each in turn carrying 2 Boeing FB1 scout biplanes. The airships would operate on a rotating 5-day cycle, with two aloft while one being serviced and replenished by the Lexington. The intention was to provide a fully independent aerial scouting element to the fleet with great range of action, but it soon became apparent the concept was flawed. Smoke from the trunked side funnels interfered with airship mooring operations, and the difficulty of confining a 700-foot airship floating within air in a rolling nautical hanger was never completely overcome. As a result, only two of the planned 3 airships were completed, and only USS Little Rock [/I]was ever permanently based on the Lexington, this from 1932-1935 until the airship was lost in a storm off Luzon. After plans to reconstruct Lexington as an experimental full-deck airplane carrier were rejected by Congress, she was eventually reconstructed as a one-of-a kind convoy raider, mounting 6 16 in guns and a large torpedo battery. She was sunk by the French Communist Battleship Normandie during an unsuccessful convoy raid off Indochina in 1942.
HMS Vanguard 1936-1960 Typical of British 3rd generation battleship construction, Vanguard and her 6 sisters formed the core of the Royal Navy's First battle squadron during the European War and the later Australian Defense Campaign. These ships were considered particularly successful, if at only 68,000 tons full load they were considerably smaller than their Japanese, German, Italian, and American counterparts. Moderately well-armored and capable of 27 knots under full power, they carried eight 1935 model 19.5 inch guns in 2 quadruple turrets. They also carried a large battery of 8 inch and 5 inch anti destroyer guns. Toward the end of their careers, the three surviving ships, Vanguard, Nelson, and Jellicoe were rearmed with multiple launchers for Supermarine Snipe televisored air-breathing cruise missles and Canadian-designed Blowback antisubmarine rocket bombs.
USS Alaska 1943-present. The 4 Alaska-class "super-battleships" represent the pinnacle of US naval architecture in the Pacific War and its aftermath. Larger and more powerful ships were built by the Japanese and Americans, but none combined the all-round attributes of this highly successful class. Displacing just under 85,000 tons full-load and capable of 30 knots at full steam, the ships were armed with the relatively small main battery of twelve 55 cal 17 inch guns, supplemented by a large battery 8 inch and 5 inch anti destroyer guns. However, the late model US 17inch gun was an outstanding weapon, arguably better than the Japanese 18, German 17.7, and Italian 17.7 weapons it was most often ranged against in the various American Wars of the mid-20th century. All four ships survived the wars and USS Oregon was converted as the US Navy's first BBBM (ballistic missile battleship) in 1962.
IJN Katsuragi 1950-1952. Katsuragi began life as one of 4 giant Haruna-class battlecrusiers, but while under design she was redesigned and modified to serve as the first of a new series "hero-missile attack ships. Unlike her sisters who shipped nine 20-inch guns on a 95,000 ton displacement, Katsuragi was completed as a dedicated carrier for no fewer than 155 manned rocket-powered cruise missiles launched from 20 armored catapults. After the Japanese defeat off Darwin and near destruction of the entire Japanese battlefleet, the Imperial Navy found no shortage of volunteers for various suicide (or "kamakazi") missions against the Anglo-American alliance. The most sophisticated approach, and one which prefigured the eventual rearming of all fleets with cruise missles in the 1970's, was the Kyushu M7A manned rocket bomb. Not only Katsuragi, but other armored crusiers and high-speed destroyers were modified or built from scratch to carry this diabolical weapon. Katsuragi, escorted by a stong scouting screen and two obsolete airships, first sortied in 1951 and succeeded in sinking no fewer than 4 Allied capital ships (USS Iowa, USS New Mexico, HMS Rodney, and HMAS Brisbane) before they could even enter gun range. She was much less successful on her next, and final, sortie as a disastrous launch explosion of one of the liquid rocket propelled M7As led to a chain reaction destroying over half the missles on the ship's starboard side and crippling the ship's damage-control capability. She was able to lanch a few kamakazis but their effect was neligible. While attempting to withdraw from the advancing US fast crusiers and battlecruisers, she was torpedoed by a British submarine, sealing her fate.