An alternate view:
I know and have met people who have worked in these "sweat shops" and I know where they are located (textiles and shoes mostly).
If the economy is bad, it is usually bad all around. In my experience, the sweat shop wages were comparable and (in most cases) superior to, what the people would have otherwise been getting had they worked in another sector (if they can find a job). The fact that these sweatshops rarely are low on workers is testimony that in many places these sweatshops are not the problem, but Third World Poverty in general is the problem and the "sweat shop" is often a better place to work than most other local places of possible employment. I have met folks who have praised God due to having a job such as this.
Of course, there are abuses and these abuses can be publicized and addressed widely when big name companies are involved....much more than the 1,000 other incidents of similar abuse or injustices at other jobs where a big name company is not involved. If Wal-Mart or Target is involved, at least there is hope of pressure/improvement if abuses are discovered (in many places there is not even any realistic way to look for such abuses..and so no one is looking, and thus not finding).
If you are trying to financially serve the kingdom, a better approach than trying to research and sort out which sources of buying are, indeed, "sweat shop" and which fall into the category of "an okay work place" would be to buy the most affordable option and then send your saved money overseas to foreign evangelists or missionaries that are caring both for the bodies and souls of these workers. Or to campaign your government to be more sensitive to the out-sourcing policies of its companies.
I would second Miss Marple's suggestion to buy at thrift stores, because then you would truly be combatting waste my recycling someone else's clothes. Otherwise, I would save any pangs of conscience for other dilemmas besides First World Guilt.