I think there are plenty of groceries stores where you will find sugarless products. I have seen plenty of that. You may take some items with you if you want, like Splenda sugar in packets, Equal etc, but you will find that in Haiti. You will also find sugar free cookies, fruits like apples, bananas etc.
What I would really advise you to do is to take with you a few bottles of water, for the first few days at least, even though they might weigh a bit in your luggage. You have to be careful with drinking water there and I would recommend that you always drink bottled water. In restaurants, ask if the ice cubes are made with bottled water. You can also ask for Perrier water or something similar.
There are some upscale grocery stores where you will find much of what you need.