You can still low carb with a moderate fat intake. It might also be the types of fats causing you a problem as well; some without a gallbladder react negatively to dairy fats but have no problem with meat fats for example.
You could try cutting out dairy to see if that helps. If it doesn't, then try lean meats like skinless chicken, fish and leaner cuts of beef to see if that helps.
And something you should definitely stay away from are sugar alcohols.
There are a few people here at least who have had problems with a higher fat intake with no gallbladder but have found that a moderate (not low) fat intake causes them no problems. You'd have to experiment for yourself what level of fat intake you can tolerate, but it can be done.
Considering that 1 can of Slim Fast has 25 grams of carb, mostly coming from sugar, you'll be getting a blood sugar spike and corresponding insulin response with each can you drink and because of that I wouldn't recommend it to anyone. You'll probably also find that you're more hungry trying to lose with Slim Fast as well (I know I sure was!) because of the blood sugar/insulin response.