Rachel, good luck with Atkins.
Stay clear of the low-carb treats during induction, and you'll be fine. There is sugar-free gum out there (I'm not a gum chewer, so I can't tell you where - I know, I'm so helpful
)
You can have alcohol on Atkins, as long as you watch what you drink. Hard liquor (gin, vodka, whiskey, etc) is zero carbs; dry wine is 2-3 carbs per glass. Beer is right out. Your body will burn alcohol first though, even before carbs, so proceed with caution, and no booze during induction.
"Moving your azz and not noshing like a pig" is a good thing for everyone, and if you only have 5-10 lbs to lose, I'd start with that and see where it takes you. If you have more than that to lose, you have to decide for yourself what to do - whether it's low-carb, low-fat, low-calorie, whatever.