I can believe this Wurst!
If you go to a low carb diet you will likely become more sensitive to insulin, and thus your basal need will drop. Also, if you don't eat any carbs you shouldn't need to inject at meals.
I frequently don't have to inject before a meal if my meal is say 30g carbs, and my BG before hand was in the 4's, or even if i know I am going to the gym I will eat a normal meal, and about an hour or 2 later hit the gym with sugars around 10, and by the time i get home they are like 4 or 5 and i get to again without injecting haha
Its doable for sure! and totally safe IMO