Even diabetics can consume carbohydrates. I understand that exercising muscles do not require insulin to uptake carbohydrates from the blood stream. Aerobic exercise is one of the best ways for a type II diabetic to manage their disease. You can take in controlled amounts of carbohydrate because your muscles will take them up and they will not spike your blood glucose levels. I had a friend with pretty advanced type II. He did frequent blood sugar tests on his own blood during rides. I got to be the control (the little jabber still pricks though even if you are a control). The thing was, my blood sugar started low and stayed constant. His started higher than mine and steadily declined through a 50 mile ride. He had to eat some source of carbohydrate to keep from getting a low blood sugar. One day we got back from a ride and he had gotten quite short tempered and highly grumpy. It was not like him. Normally he is well mannered, placid tempered and good humored. I looked at him and said "stay right here". I went into my house, I got a small glass of orange juice (about 4 ounces), gave it to him and said "drink this". A few minutes later, he was back to normal.

Eating oil or fats will not help your body maintain its carbohydrate equilibrium. Of course, diabetics often respond quite differently to different foods and situations.

Fat will fuel your body at about half power. Your climbing sounds more intense than that. Your climbing has to be partially fueled by burning carbohydrate. You body will either use its glycogen reserves or catabolize protein to make carbohydrate (not a really good thing).

Think about trying small measured doses of carbohydrate. GU is a good source.