Thanks so much for the answers to my questions.
It probably doesn't help much to know that many owners of small dogs have dietary issues. They frequently don't want to eat kibble after they've gotten a taste of table food or are just fussy eaters to begin with but in this case, at least, you've found food which she will eat (since she's carrying extra weight).
And, weight gain is a common problem after a dog has been spayed since we've removed hormones which can help to increase the basic metabolic rate (similar to humans who go through menopause).
This isn't to say that nothing can be done about the weight gain, just that it's more of a challenge to get them to lose it.
To answer your specific question, no, I wouldn't put down kibble and hope that she'll eventually get hungry enough to eat it. I'm not a huge fan of this method of "forcing" a dog to eat what they don't like.
If you want to try and transition her back to a commercial, prepared dog food (not raw), then I'd try some of the semi-moist or canned versions since there are so many options out there. She may find these more palatable than plain kibble.
I don't want to get into a debate about the pros and cons of a raw diet but it sounds like it may not be completely balanced if it's not specifically formulated for dogs (I'm not sure if this is true or not). But, if that's the case, then if you continue to feed raw, then you might want to supplement with a daily vitamin/mineral supplement which can be purchased on most pet/grain stores or online.
But, regardless of what you decide to feed her, a weight loss program for dogs is quite similar to a weight loss program for us: you need to consume fewer calories and/or expend more energy.
By my calculations, she should be eating about 400 calories a day or just a little less. I don't know if you're going to be able to calculate the calories in the raw food you're feeding her but this information is usually readily available for the commercial brands (although sometimes you have to do research on the internet or call the company for this information since it's not routinely included on the ingredient label).
And, all calories count. Treats or other food fed should constitute no more than 10% of the calories fed per day which is going to be about 40 calories. So, it might be prudent to determine the number of calories in her training treats and the chicken wing she eats.
Perhaps give her 1/2 to 1/4th of a treat rather than a whole one, for example.
And, exercise is important as well. Perhaps increase the number of walks she takes if you can't increase the length of them. Continue to play with her in the garden. I'll take pity on the cats and birds and not suggest that you encourage her to chase them but anything to get her moving such as regular, daily play with her friends at the dog park would be great.
Once she starts losing the weight, she may have more energy and she'll want to walk/play more.
I'll mention my ideal body weight for a dog which isn't determined by the weight on a scale but rather by how her ribs feel when you run your hands down the length of her ribcage. You should just be able to feel those ribs without having to poke to find them. So whether it's 1 kg or more that she needs to lose will be determined by how she feels after she's lost 1 kg (which hopefully she will lose!).
She's young enough that I'm optimistic that you can get her to the ideal body condition regardless of what you decide to feed her.
I hope this helps. Deb