Why a Q-ship at all? Or rather Merchant Raider, since a Q-ship is a countermeasure. Now, historically the success of raiders have been pretty much directly related to the level of communication available. Compare the German raiders of WWII with the works of the East Asia Squadron of WWI. Despite not being able to camouflage themselves to any useful degree, the East Asia Squadron had far greater success than their WWII descendants. Now, it can be argued that this was because they were actual warships and not converted merchants, and to a certain degree this is probably true, however the real reason why they were so successful was the communications lag. By WWI radios were still a rarity outside of passenger liners and other high profile ships and those that did have them usually only had one operator and they typically shut the radios down when he was off watch to save the tubes. (SOLAS didn't really catch on until after the war) On top of that, truly long range radio wasn't really a thing yet, so long range traffic had to go through easily cut undersea cables. In comparison, by WWII radios were widespread to the point where merchants usually had two sets, international law had changed so that all ships were required to keep a 24 hour radio watch and long range radio communication had become much more simple. This means that the ships assigned to hunt down the raider can be much better coordinated and they'll be acting on much fresher information. Advances in aviation and later radar means that the ships themselves can cover a much bigger area as well.
Wind forward to today where every ship engaged in international trade is registered and a simple search will give you plenty of pictures of them. In between that and sattelites, AIS tracking, GPS tracking, the widespread adoption of maritime reconnaissance planes and coastal radars, panic buttons etc etc etc and you find an environment that is positively hostile to a raider.
And all that assumes you'll be able to buy the ship and converting it without anyone noticing it in the first place.
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