Chorlton and Didsbury have their share of crime too just not as much of it. I have lived in chorlton all my life and in terms of crime have been very sheltered but I still know quite a few people who have had problems here.
Wythenshawe has some very annoying problems because about 10% of the population seem to be real chavs which seem to create 95% of the crime there.
If you want a real sheltered live then move to Hale, Bowdon etc but it would be a very boring existence.