Your goal to lose over 10 kilos in a month is not healthy. It's not recommended to lose more than a kilo a week, and by that recommendation, you wouldn't even reach you goal in 2 months. Is it that you NEED to lose 11 Kilos before September, or is that you want to? Because if it is that you need to, then I'm sorry, you are out of luck. Now if losing weight is more important than managing it before the date, you can lose it over the course of 2 and a half months.
I can't say I know for sure if using Wii Fit actually works in terms of losing weight, but I don't see why not. BUT, Exercise is only half the work, you also have to make sure to EAT RIGHT. If you eat bad food you counteract the exercise and then you are right where you started. Drink LOTS of water. Cut the carbohydrates, sugar and bad fat. Log what you eat and drink. Plan what you eat. And if you don't know what to eat, research, research, RESEARCH. Also, don't starve yourself, it will give you no energy to exercise.
This is everything I've learned in my journey of weight loss.
I hope it helps, and I hope you put it to good use.
Exercise is really important but with the exercise you also need a good diet that's both nutritional and low in saturated fats and sugars :) I also think that it would be difficult to lose that much weight in a month so in order to not cause any bad side affects to your body and so that you're not disappointed if you don't reach your weight goal I suggest that you give yourself a bit more time because at the start of a diet you always lose a lot however, it gradually decreases, hope that helps :)