The words "wielded" and "exerted" are similar, but they are not always interchangeable. In this sentence: “…Uruk, would have wielded more influence…” “Wielded” is the better choice. It means to have and use power or influence, like holding a tool or a weapon — it's often more active and personal. “Exerted” means to use or apply something, like effort or pressure. We can say “exert influence,” but it often sounds more formal and is used when talking about applying influence in a specific situation, not just having it. So, yes, you could say: "...Uruk, would have exerted more influence..." …but “wielded” sounds more natural here, because it suggests Uruk possessed and used influence over time, not just in one moment. “Wield” = to have and use power or influence (often sounds strong and active) “Exert” = to apply power, influence, or effort (often sounds formal or technical) In this sentence, “wielded” is the better choice.

In this context they would be very similar, but 'exerted' sounds inappropriately too 'active', as if it should be talking about a specific moment, a specific event of applying force against another body; while 'would have wielded more influence' is a bit more about long-term potentiality, ie, strength and the ability to exert without necessarily exerting it. Having said that, they are both active words, so the difference is minor. Just in this type of context, the difference comes alive. Use exerted for applied force; use wielded for simply holding up the sword without necessarily striking anyone with it yet.