While undertaking the Searching Sakai mission in Assassin’s Creed Shadows, you’ll be tasked with conversing with the gunsmiths, which presents a series of choices. Pay attention as you eavesdrop on Asajiro and Yakichi—critical information for one of the choices will emerge here. After the dialogue concludes, engage with them again. Below are the optimal choices to make, along with the implications for My name is not important or I am with the Imai.
Additionally, a follow-up question will arise, granting you the option to respond with either a menacing reply or to offer a bribe.

My name is not important or I am with the Imai.
This segment of the discussion isn’t significant. Selecting “I am with the Imai” is a deceitful choice, evident from the scale icon, yet you will still face a follow-up inquiry (details below). The decision on whether the NPC believes you is determined by the game’s design, requiring you to proceed with the dialogue to discover the outcome.
Imai Sokyu’s Offspring or Is It None of Your Concern?
Following your initial response, the gunsmiths will query you with, “Who is your contact in House Imai? Sokyu’s son or his daughter?” You can select from three potential replies: I know Imai Sokyu’s Son, his Daughter, or That’s none of your business. Given that earlier in the scene, they were discussing Sokyu’s son, it’s advisable to choose that option.

You’re Wasting My Time or Should I Pay a Bribe?
Ultimately, you will be presented with the choice to either pay 500 Mon, indicate that you lack sufficient funds, or state that you’re wasting their time. If you opt for the ‘wasting time’ response, the brothers will flee, prompting you to pursue the one indicated by the marker. You can eliminate him and secure the contract from him.
On the flip side, choosing to pay the 500 Mon will instigate a brawl between you and the brothers. This encounter should be manageable, and once victorious, you can loot the contract as well as the 500 Mon.
In conclusion, the most straightforward and efficient move during the Gunsmith interaction in AC Shadows is to deliver the threatening response, enabling you to swiftly chase down Asajiro and execute him to obtain the contract.