I have never seen props changed on "Big" ships. I do remember a story of one ship in the P&O group that had the original prop replaced with one with a lesser pitch because the engine was overloading on Torque before it reached it's rated RPM and so could not develop full power. The original Bronze prop was kept as the spare and lashed down on top of the aft Deck House alongside the emergency steering position. When the ship went for scrap someone remembered this valuable lump of Bronze and it was discovered it been miraculously converted into carved Wood with a realistic paint job. More of the "Dark Side" forces at work?
As a Junior I sailed on the old Merkara aka Strathmeigle, she had the same problem of the prop over torqueing the engine, and could never develop full power or speed, she was on a General Cargo run from the Persian Gulf to Kiwi and Aussie, but was going on to a container run through Suez and they wanted maximum speed. They cropped the tips of the prop blades, increasing the slip and so reduced the Torque at any given RPM enough for the engine to make max torque at maximum RPM and for the ship to reach its designed speed, but at a slightly reduced efficiency.
With CPP obviously there would be no need to change the prop, just increase or reduce the pitch. Usual thing, if the Exhaust temps are too high, you phone the Bridge and ask them to reduce pitch. 10 minutes later they, they think you have forgotten about the exhaust temps and put the pitch up again!
Obviously with CPP there is usually an overload device on the fuel rack which will automatically send a signal to "Shed Pitch" or "Reduce Pitch" when a lever on the fuel rack hits a micro switch or a potentiometer rotates to a certain position, preventing the engine being overloaded. You often see this flashing in heavy weather when the Deck Officers try to force the ship at full speed through heavy Seas. Of course this only works if the individual fuel racks for the pumps all remain set exactly the same as when the pitch reduction system was set up and nobody has changed the lengths or the spline positions on the Governor shafts.
This system would obviously prevent overloading from any cause also it is rare for commercial shipping to run at more than 85% power.
I have also seen on supply boats with big electric bow thrusters and cargo pumps driven by shaft alternators, a system of " pitch limiting" which works entirely separately. For instance if the breaker for one Bow Thrust is put in, the pitch control "desired Value" signal from the Bridge is restricted to a maximum of 80%, if the second BT breaker is put in, it is restricted to 60%, appropriate reductions are also made when the breakers for the heavy consumers i.e. cargo pumps and Bulk compressors are put in. These reductions are related to the power of the engine and the power demand from the consumer, and will often be different from the ones quoted as an example, but will prevent the combination of Electrical and propeller load overloading the engine.
It is always better to ask a stupid question than to do a stupid thing.