Like
Rana said, reducing sugar will not result to weight loss. Eating less, or creating a caloric deficit, will.
Some people do see body recomposition changes (esp around the midsection) if they rearrange their macronutrient ratios. Usually this means reducing carbs and increasing proteins.
However, to be totally honest, your BMI right now is already on the lower end of normal. Cutting weight will most likely result in your ending up a smaller version of yourself right now (in other words, the last bit of "stubborn fat" spots are unlikely to be affected at this stage as you lose proportionally all over) What is concerning though is that weight that you lose at this point will include a decent amount of lean mass loss (from the muscle, bone, etc). This not only doesn't affect the appearance changes you're hoping for, but isn't great for your health.
What you may want to do instead is focusing on eating at or slightly above maintenance calories (not trying to create a deficit) and work on strength training. There are tons of success stories on this forum of women who have reshaped their bodies by lifting heavy and eating well with lots of protein. Their weight stays the same, even increases a few pounds, but because that weight is lean muscle mass and not flab, they look smaller and leaner. Women can make pretty impressive strides in their midsection through these strategies.
Good luck!
PS Reducing sugar is always a good thing- way to make some great changes in your diet