For doing a scrappy binding with squares this small, you'll have to do a straight seam (although in any other situation I'd do a bias). Reduce your stitch length, use a neutral thread and press seams OPEN to reduce bulk then it will be fine. You might want to try and prejudge at what point you're turning corners too (unless you pre-pin which I don't!) as it will be tricky to avoid a seam at the corner when it's this scrappy.

less bulk on the seam

Do as you like, I usually use straight seams

Straight seams for me:)

Considering you have two different colors it really wouldn't make a difference because it will still be noticable. It's hard sometimes to do the traditional method when you are tight on fabric. As long as it looks good to you that is all that matters.

Presume that your original binding was not cut on the bias?

Agreed, diagonal lays better.

For durability in a bed quilt, my binding is folded in half before sewing on, so I prefer joining the binding pieces on an angle. I find it lays flatter and you don't have a bulky "bump" in your binding. But when you are piecing a binding of different fabrics, joining the pieces straight is your only option. I usually press the seams open flat, then trim them a little closer than 1/4". Pressing is everything. If your quilt is for decorative purposes and won't get a lot of wear, you don't need your binding doubled and can do any method since you won't have as much bulk. Good luck!

I use the angled seam most of the time but I also have made a binding from squares, what you have mentioned, and I used the straight seam...and it turned out just fine........

Your quilt, your rules !!!!!

Sewing a butt seam on binding creates a very bulky lump. By seaming it on the diagonal the bulk is mostly eliminated