While a lot of fictional spies do indeed engage in a lot of hand-to-hand combat, it's not what makes them stand out among other action archetypes. Stealth, gadgets, concealed weapons and intel are what separate them from other action heroes, martial artists and superheroes. All Pokémon fight, but it's how they fight that informs their type(s).
I also don't think they'd have chosen a chameleon, an animal known for its ability to become almost "invisible", if Fighting was going to be the focus. The first trailer even drew attention to Sobble choosing to hide from Grookey. And of course, we know Scorbunny has a lot of Fighting moves and is likely going to fulfill that role in the trio, whether it actually receives the type or not.
Yeah, admittedly, it's a stretch.
These characters are not above hand-to-hand fighting, however. Rorschach in
Watchmen is a hardboiled detective who gets into a lot of fistfights with gangsters, though the behavior of the other characters suggest this is a negative character trait, that he has a lot of pent-up rage and takes it out on said gangsters. The idea is that pretty often, in spy stories and detective stories, the protagonist gets caught, a bunch of thugs show up, and he or she has no choice but to actually defeat all of them to move onward. It's not a major part of these stories, but they're there. Both archetypes' general style, if they have nothing to assist them, are old-fashioned fisticuffs, with no formal training (and James Bond has had to do this many times). There are Fighting-types who embody this fighting style: the Mankey line, the Timburr line, the Scraggy line, the Pancham line, and the Stufful line.
I don't think it'll gain the Fighting-type. There are few to no Fighting-type moves that would work with the spy theme, since most of them are about refined, practiced punches and kicks, and while the likes of James Bond and Batman have learned martial arts, it's not a defining part of themselves, and they only use it as a last resort or to quickly subdue an opponent when in a hurry. (And most writers just have them do said fisticuffs anyway.) I think the Ghost-type would be the most fitting, since spies fade in and out of existence as if they were ghosts, though not literally.
By the way, though chameleons that change color can do so to camouflage, and they're intelligent enough to camouflage to multiple textures at once, more often, it'll change colors to indicate its mood. For instance, when angry, they turn black with brightly colored speckles here and there. And, as it seems, they're prone to getting very angry when encountering other chameleons, as a lot of such species are territorial (specific to each other, not to other animals) and will duel when they meet, fighting by slapping each other.