I would be okay for 30 miles on just water (though I normally mix in 1/3 OJ because I like the taste) but I know a lot of people who conk out very quickly if they don't keep topping up their energy reserves while riding.
On longer rides (30+ miles) I do use carbo-drinks but I still lose weight at the rate of about 1 pound per 100 miles cycled.
I suggest that you experiment with weaker and weaker drinks until you find that you don't quite have enough energy to finish your rides comfortably. Go back one step and you should be taking in the optimum amount of fuel for your rides.
Except perhaps when sprinting flat out, you will always be burning some combination of glycogen (carbs) and fat. Since you are trying to slim, you don't want to be replacing any of the fat but that is what you are doing by taking in excess carbs (any not needed would be stored as fat).
At 6' 1" and under 13 1/2 stones I doubt you really need to lose more weight!?!?
I am the same height and just dipping under 14 stone in the last few months and really don't think it would be necessary or wise to intentionally try and get much lower just for the sake of it. I personally reckon floating around between 13.5 and 14.5 stones during the year (up a bit at Christmas then down a bit during the summer when I do most cycling) is a reasonable state to maintain.
I'm also 6' 1" and at 13 1/2 stone I am still significantly flabby. You have to take individual build into account.
I'm a medium build. I don't have a neck wider than my head and I'm not built like the proverbial brick sh*thouse. On the other hand, I am not naturally scrawny like Andy Schleck either.
My avatar photo was taken when I weighed about 13-and-a-bit stone. I was getting pretty slim, but I still had a 3 inch roll of fat round my waist. I reckon my optimum weight is about 12 1/2 stone. Below that, I look gaunt and lose strength.