Don't worry too much about calories burned. Unless you're talking a difference between 100 and 500, it's not really going to make enough difference to matter.
Firstly, because weight loss is mostly diet. Exercise contributes only a very small part of your total daily calorie burn, so a marginal increase or decrease in it doesn't have a very significant effect on your results.
And secondly because everything's an estimate. From your BMR to how much is in the foods you eat, to your exercise burn, everything is only an estimate. Every one of us is likely to be 'wrong' by a couple of hundred calories every day no matter how exactly we try to track things, and the figure we're 'wrong' from may even be not the right figure for us personally because the goal is an estimation.
Actually, you probably burn more calories walking around day to day in everything else you do with a limp or the stick than you save by using the stick to support your weight a little during exercise. I'm not sure about stick-supported-walking, but I know that when I'm injured and I limp - boy does that work it more than just plain walking! :)
Deb, in New Zealand