You do not need to be on Atkins. period

If you do need to lose 10 lbs do it by working out more or eating less calories. You do not need to be in ketosis so forget about induction.
The reason you are not supposed to eat sugar free candy during induction is to break a possible addiction. You do need to bust this sugar addiction and there is a supplement that will help you L-Glutamine - buy it and read how often they recommend taking it.
Get your sugar from natural fiber rich sources- FRUIT !
Try keeping fruit around instead of these sugar free sugar alcohol candy.
You should check out the Zone diet it is more appropriate for someone your size and weight, or someone who wants to maintain a low weight for life. Going into induction may be counter productive. If you added 2 runs to your week you would drop 10 pounds faster than you would on Atkins.
Same if you did pilates etc.
Cutting out refined flour and sugar is the best thing you could do for your health long term anyway. Check out most Asian cusines, there are no refined products except sugar which is mainly used in American Chinese food and otherwise comes mainly from coconut milk which is a natural source when unsweetened and totally fine !
Those 10 pounds could be anything, water,, muscle....do not obsess about it ! Its a number !!!

Check out your body and if you want more shape run more or do another workout geared to the shape you want.
Please dont go on induction, it is silly. But eating the way Atkins recommends you do is not so silly-no refined products including sugar is a healthy way of eating.
Good luck and I mean all this in the best way while hoping for your happiness with the way you feel and see yourself.