The Brits took all sorts of very real suppressed revolvers away from the IRA. You get some noise from the barrel cylinder gap, but a .22 isn't that loud anyway.
It depends on what you mean by a spy. Real spies, engaged in the act of gathering intelligence, won't make it a point to go about armed. For years CIA agent training was simply firing a few rounds out of a Chief's Special more or less just to say that you had.
Things are a bit more complicated if you lump various and sundry other agencies doing various sorts of intelligence/counter intelligence work into the "spy" category.
(Fun fact for those that haven't been around, the really nefarious stuff happens when a salary is paid by the Department of the Interior, not the DoD or DHS/what not. Has to do with legalities related to war crimes, etc.)
Call sort of thing "Men in Black" work for convenience. Some will have agency issues guns - Sig P229Rs were popular for a while, in .357 Sig. Copying the Secret Service I suppose. In the 1990s, sometimes sterile guns were used, trade in guns from other agencies, surplus from their orders, or officially ordered by other agencies. Circa 1996 a number of 92D Centurions with night sights dated three or four years earlier were floating around in such circles. Well before parts kits and AR building was popular, "inhouse" made CAR15s and A1s were also kicking around. The receivers would be completely sterile - no markings at all. The rest of the parts would be GI or commercial.
Suppressed Walther TPH or Beretta 950s (the long barreled ones in .22 short, stick them in the ear) would be something that would turn up years ago. Later a can on a Walther P22 or an integral unit on a Ruger (ever popular).
Revolvers.... Maybe actually. During that brief period when the 317 was the lightest game in town (back before it even had a lock). They used to be shown at trade shows hanging from a balloon and you could hang one around your neck via a lanyard. Something like that would have been carried on a low key "human intelligence" assignment if working domestic. Doesn't scream "cop or Fed" and is easily hidden. They were more reliable than the small .22 and .25 autos.
They're not that noisy, even with a short barrel. A room away, fired indoors, the signature sounds like a cap pistol went off.
