I'm pretty sure I've seen a ruling allowing this, but I can't find it anymore. The case that inspired the question this time was this: some TAGs can hit AC2 with their EXP or DA (and thus Anti-Material) weapons, others - with their fists (as specified in season 10 missions), but, for example, Guija and Xeodrone have AP CCW and Heavy Pistol, which are not inherently Anti-Material, but having them, technically, makes them unqualified for the whole "has no CC weapon" clause.
See also Raoul/EM CCW Morlock when the target is already EM'd: he's got better odds slap fighting. No ruling but consensus is yes.
Is Bare-handed a CC capable weapon the model is equipped of? Yes. Should a model equipped with 5401652 different CC capable weapons be able to choose one of those when performing a CC Attack? Well, it's the purpose of bringing all of them along....
But Bare-Handed isn't Anti-Material? Why? The damage is PH-2 with Bare-Handed. Maybe you mixed E/M SSW with E/M Ammunition, because the Ammo is just E/M, but with CCW it is N + E/M, so CCW is still better than Bare-Handed because the damage is higher.
Because of CC over 20. Criticals with E/M CCW are weird. Auto E/M effect + roll for wound. Bare handed gets auto wound.