A shag cut is a technique that uses various choppy layers to create fullness in the crown, and thin fringe around the edges to frame the face. It’s been around for years, so to make it look new and modern, try a punchy color like a bright red to elevate it.
You are very blessed with your square face, very strong and many celebrities have this shape. For your hairstyle you have to choose which one could soften your square face. Many woman with this shape choose medium to long hairstyles
For business women who want to look elegant all the time, you can choose short bob hairstyles. Which it still in classy hairstyles, no texture and stay sleeky.