Isn't this just a standard use of an ability check? Surely it would be the DM's call?
I would recommend not.
I'm not seeing any theme of genius gadgeteer or expert craftsman in this class. No reason that someone of this class would have the ability to make high-tech or magical devices where others who could also use those tools could not.
Sounds like a subclass option.
Its not weird that your concept of an assassin needs an explanation. - It is very different to many other people's concept of what an assassin is. I think that the image of the assassin in many people''s eyes is the consummate professional, who does the job with a minimum of fuss and risk, ensuring they escape to spend their fee. Terry Pratchett's Guild of Assassins for example.
The archetype that you seem to be using, of someone who fights their way through hordes of minions to openly confront their target - just isn't what the word conjures up to a lot of people. "Hitman" or "soldier" might be their words for that concept.
Any example that uses firearms it tricky because their deadliness varies by genre, and D&D is enough of a genre of its own that trying to shoehorn any particular non-D&D example into D&D terms is going to cause issues.
Bond from the books is a definite Assassin. Film Bond depends a lot on who is currently playing him.

I think methods are probably the best indicator of class, since gunplay is hard to use as a measuring stick, and most films involve what is fairly obviously a high-level character mowing down low-level minions.
Single, telling attacks from stealth and then disappearing are more assassin-y. Planned and prepared situations to remove someone who is well-defended seems like the methodology of an assassin, even if the plot means something goes wrong and they don't pull it off flawlessly.
If the character is shooting or disabling enemies rapidly, with occasional bursts of almost-superhuman effort or resilience, that's a fighter. They may use stealth and cover, but if the people they kill are often face-to face with them - fighter.
Hence the issue with trying to visualise what you're trying to do. I'm only familiar with two of those examples. To me, Waylander is very much a Rogue. In 5e, Artemis Entreri is canonically a Fighter.