As someone else has pointed out, short-ranged, land-based planes could be, and were, delivered to remote islands disassembled and packed in crates. Any kind of cargo ship could accomplish this, often the crates were carried as deck cargo. The disadvantage of this method is that the planes have to be reassembled and tested before they can be used. This requires skilled mechanics and the necessary tools, but these can also be delivered by the same types of ships. The assembly process and testing routinely took 2-3 days, but could be accomplished in 24 hours if necessary.

Assembled and flyable aircraft, to be used immediately, required a flight deck to be flown off of. But if berthing facilities were available and equipped with cranes of the required capacity, the ship might come alongside a pier or dock and have the planes lifted off the flight deck and transferred to the dock. Many small islands had no such facilities and the preferred method was to have the planes flown off and land directly on the airfield where they were to be based.

Even if the US lost all it's fleet carriers, it would still have two aircraft transports in commission in December, 1941, the Langley and the Long island, which could deliver assembled fighter aircraft to island bases. The Langley's flight deck had been partially dismantled in compliance with provisions of the Washington Treaty, but it could have easily and quickly been restored upon the outbreak of war. The Long Island was the prototype CVE and actually was used for delivering fighters and other planes to Guadalcanal in 1942. Fleet carriers were also used for such duties at times, notably the Wasp and the Ranger in the Atlantic.