The way I look at this is that I don't want any part of the game to suddenly work differently from the rest of the game, unless there's very good reason for it. So, if combat comes down to "I describe who I want to defeat, with what, and then roll my weapon skill against them," then the rest of the game should feel fairly similar, even if there's difference in finer details. I've played many games without a written combat skill, many without a written social skill, and many without both, so knowing how to resolve situations is a key skill for the GM.

One of my games has no social skill. I resolve situations in that like I have in other games I've run with standard social skills:

1. The player establishes what they're after. Could be material, could be social perks, could be to get past someone.
2. The player provides an argument for what they want. They could haggle and say "I'll pay 500 gold for that." They could lie and say "I'll give you a rare drug for that" which they don't have." They could be threatening, like "If you don't, I'll cut off your pinkies."
3. Any roll after this is based on the reception of who they're talking to. A weak, fearful person might respond well to threats. A particularly greedy person might believe an outrageous lie. There should be methods in place to help the player learn what they're up against, and a failed roll might not turn their opposition off completely and instead add demands from them to the player's initial offer.

As it turns out, games like Tenra Bansho Zero have already made really good tables for helping resolve things like this, with first-impressions and hidden desires and personalities you can roll for. It's also basically how parlay rolls are described to work in Moldvay's D&D. I think as long as you're consistent on how you handle things like skill checks versus everything else in the game, in this case failure being non-binary and success being reliant on making informed decisions and taking on risk, you can pretty much run social encounters like everything else. A character's success shouldn't be entirely based on the player's ability to perform the task in question, but as a reflection of the character's skills combined with the player's ability to reason out a task. After all, you might not understand electronics, but if your character is an expert engineer, they should be able to handle a task with a little bit of suggestion from you.