"something that doesn't wobble too much while walking"
This is going to be a problem with any cheap camera. The problem is the lack of image stabilization. Most of the mid-range shooters have digital stabilization but nothing is better than optical stabilization. It's your requirement for AA batteries that going to keep you in the super low quality camera range. You may want to reconsider this.
In my opinion the Canon PowerShot S95 is the best all around point and shoot. It has an excelent image sensor and performs very well in low light. It also boasts optical image stabilization and 720p video. Let's not forget Canon's excellent optics. (forgot to add, it shoots RAW, for any photo geeks reading this).
A lot of the flip video style cameras have a fixed focus pinhole sized lense. The image quality is poor. They use digital zoom, YUCK!
I'm just thinking from the mindset of 1 camera to do it all. I personally would not want to pack 2 cameras.