We use all sources for energy, all the time. During the 4 hours after a meal containing 100g glucose its estimated that energy is supplied by 60% CHO, 25% fat and 15% protein
During exercise after an intial demand for glucose to get going, if we then exercise at low intensity we use the greatest proportion of energy from fats . As exercise becomes more intense, more energy from glucose is used.(and demanded) , we still continue to burn fats though.
If we get to be flat out at near max heart rate almost all the fuel needed is from glucose. Then there is a big demand, thats why anaerobic exercise can increase glucose levels.
(I started writing a complex explanation then found this:
http://www.dummies.com/how-to/content/b ... rning.html
What's a gentle walk in the park for one person though could be quite intense for a less fit person. Some people when they start exercising are working at quite a high heart rate. It is at above about 60% of maximum heart rate that the demand for glucose gets higher. If you haven't been exercising you could reach this level with a moderately intense walk. Exercising regularly ie training means we get more efficient and don't demand so much glucose at lower intensity levels. As we get fitter our resting heart rates should fall.
In T2 diabetes there often seems to be a bit of an imbalance ie glucose is demanded but too much glucose is released; the classic liver dump' . Basically, the 'glucostat' of insulin/glugagon aren't working to balance each other. It could also be that the glucose though present, doesn't get into the cells, because cells are very insulin resistant .(
though during exercise this shouldn't be problematic since insulin is not needed to get glucose into the cell when exercising... unless glucose levels are very high before exercise and that's a whole different scenario)
(have you any idea where your blood glucose level is during or at the end of the exercise?, this could make a difference to possible solutions)
The only practical ideas are and just ideas (sorry)
a) keep on :exercise does reduce insulin resistance and should lower levels over all.
b) maybe walking/ swimming at a lower intensity until you are more 'trained'. You could get a heart rate monitor and see how intense you exercise actually is.
c) (and sorry this isn't a low carb piece of advice!) It might help to eat a very small amount of carbs (10-15G), such as from fruit before exercise to help fuel the exercise or a similar amount during the period imediately after exercise when little or no insulin is needed to use it.(thus if there is a dump; preventing it)