So type 1 vs type 2 isn't perfect around the edges. You have to take out the genetic causes of DM (MODY and neonatal DM) because they may look/present like type 1, but can often respond to orals (depending on the mutation). Even removing those, you can end up with the classification of ketosis prone type 2/type 1b, which are type 2 phenotypically but many have aspects of type 1 (such as antibody positivity or a propensity to go into DKA), and may or may not be absolutely insulin requiring.
Your described patient is a bit on the other side, phenotypically type 1 but with significant insulin resistance. Let's assume that you make sure he's not truly a type 1: you get a c peptide (and it's detectable) and 2 or 3 antibodies (which are negative). All right. So you have a skinny guy with type 2. Why?
It helps to separate your ideas about weight from metabolism. Normal weight people are more likely to be metabolically healthy and obese people are less likely to be metabolically healthy, but the correlation is not absolute.
You can have a morbidly obese individual, BMI 50, who has a normal blood pressure, a normal fasting glucose, and no fatty liver disease. We've all seen these people, many of whom have been that big for years and years, without any sequelae of obesity. These people are obese but metabolically healthy. They probably have some increased risk of disease, but not nearly what you'd expect given their size.
You can also have the opposite, which is what you're describing. A skinny person who is metabolically unhealthy. What is the cause of this? Well, some people are just unlucky. There's tons of genetic variants that make you more prone to type 2, and it is pretty strongly hereditary. Part of the picture is when these people gain weight, they have a propensity towards gaining visceral fat rather than subcutaneous fat, which gives you all the metabolic consequences without making you look obese. You also tend to get more insulin resistant as you get older, independently of gaining weight.
What else could be the case? Well, there's also the possibility that he's not actually THAT insulin resistant, but there's something wrong with how he's absorbing or processing insulin. Assuming his injection technique is correct and he doesn't have significant lipohypertrophy, you have to wonder if there's anti-insulin antibodies. Clinically significant titers of those are pretty damn rare in modern times though, so it's much more likely he's just more insulin resistant than you'd expect given his BMI and age, due to a bad luck of the genetic draw.
Depending on the patient and their comorbidites, you treat them just like you would any other type 2. If they're really poorly controlled they will almost certainly need at least basal insulin, but a lot of the time you might be able to get away with basal+orals. It's really patient dependent though.