Okay, so a lot of media screws this one up. Interpol is a just an advisory agency. Today it’s a part of the UN, though the organization actually dates back to the 1920s (as the International Criminal Police Commission).
They have no actual law enforcement powers of their own, and they have no direct involvement in criminal investigations. Interpol agents pass information to governments and function as administrative liaisons between national law enforcement agencies.
Today, Interpol is mostly just the curator of multinational databases, including things like: fugitive warrants, arrests, fingerprints, and general crime statistics. Interpol Agents are more likely to be tasked with assisting local police in actually having access to, and being able to use those databases, than being asked to consult on specific crimes.
If you’re doing sociological analysis of criminal trends, they’re actually a fantastic source, but, they don’t actually do anything.
They’re not spies, they don’t hunt down criminals across national borders, showing up at crime scenes unannounced. They push paper around. That isn’t to say their services aren’t useful, but they’re not some kind of transnational FBI agent.
Further, Interpol does adhere to the UN Declaration of Human Rights, which pretty quickly takes out your “covert assassin” concept at the knees.
If your character is a spy, an Interpol Agent would actually be a pretty terrible cover, unless the intent is just to bug a police detective’s office, get out, and disappear. It’s not a cover they can take into the field, doesn’t provide much freedom of action, and Interpol won’t authenticate it.
On the question of stealthy weapons, one of those things doesn’t depend on an explosion to function. Which will make it much quieter. But ultimately this is a “right tool for the right job” kind of situation.
Remember, in Europe, tight gun control is the norm. If your character is caught by local law enforcement with a suppressed weapon, that’s probably going to be serious jail time. I’m not sure what the fallout from an Interpol Agent going off and operating as a vigilante would be, but the scandal would almost certainly massive.
If your character is going the spy route, The Bourne Identity might be worth reading. Even if you’ve seen the film, dig up a copy. It’s not a fantastic book, but there’s a lot of basic tradecraft in there.
If you’re willing to dig through RPG systems, AEG’s Spycraft core books can work as a basic primer for writing espionage themed fiction, including what you’re describing. The core books are somewhat agnostic on the martini/stale beer spectrum, but, they do specifically provide information for stories of both varieties.