Below is a link to a YouTube video of the type of air rifle my assassin will have in QUEEN'S GAMBIT. It is based upon an Austrian model used by elite snipers at the end of the 18th century. Lewis and Clark took one along with them on their expedition. While not silent, notice how much quieter the report is versus a conventional gunpowder fueled weapon. The man in the video isn't even wearing any hearing protection. While you could certainly hear this on a quiet day in the country, in a crowded city with a cheering multitude and bands playing it would not be noticed.
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The next one has a nice short video about the Lewis and Clark expedition and the air rifle they carried.