That’s an interesting question. The fantasy archetypes I provided were mainly based on the character classes in World of Warcraft—rather than on pen-and-paper RPG’s—as I realized they matched up quite cleanly to the weapons in Secret World Legends.
An assault rifle build without grenades is possible using the Hellfire Assault Launcher weapon, but neglecting grenades is not recommended for end-game group content, as you’d be giving up a lot of damage output. If you’re not concerned with end-game group content, then it’s not a problem.
If you pair it with dual pistols, you gain the ability to debuff enemies using Trick Shot and Kill Blind (although there isn’t much need for debuffing in solo content), and Trick Shot is a better elite than assault rifle’s Red Mist. If you pair it with blade, you gain the melee weapon aesthetic, but it’ll be important to get a Stormbringer or Soviet Techsword to ensure adequate damage output. Both dual pistols and blade have a strong healing active, so survivability won’t be a concern.
If you have other RP-related requirements in mind, you might want to try posting a new thread to get some input from the RP community around here.