Where are your facts on this? I could be wrong but didn't all wing guns simply have a trigger and thus fired at their cyclic rate?
This is correct, the OP is wrong.
Spitfires, for example, could fire the cannons, the machine guns or cannons and machine guns together. Whatever was being fired simply fired at its cyclic rate.
EDIT:
It occurs to me that the OP may have been confused by reading about synchronized guns and misinterpreted what that meant. Synchronized guns are mechanically or electrically interrupted so that the bullets do not strike the propeller when they gun is mounted within the propeller's disk. This causes a reduction if the rate of fire of something like 10-40% depending on the type of gun. Examples of synchronized guns in AH would be the machine guns in the fuselage on the Bf109s, Fw190s, A6Ms, Ki-84 and Yaks and the cannons on the Ki-61, La-5/7, inboard cannons on the Fw190s. Guns that were outside the propeller's disk, such as on the P-51, Spitfire, P-47, F4F, N1K, Hurricane, F6F, and so on do not need the interrupter gear and thus fire at their full cyclic rate.