Alternative yarn for pattern

I have received a commission from my mom for a capelet, for which I found a beautiful pattern. But, the yarn the pattern was written for no longer exists. That yarn was a #6 Super Bulky, 11sts x 15rws (4x4inch) on 9mm needles. The yarn I selected is a #5 Bulky, 12sts x 16rws (4x4 inch) on 6mm needles. I’m trying to work out how to adjust everything to make sure that the capelet still comes out to the right size. Would it work if I just switch over to 6mm needles? Thanks again!

I’d try a swatch with the 6mm needles and see…

First, try a sample in the needle size the pattern needs, then adjust from there. It works best if you try for the gauge in the pattern, rather than the yarn label. You may come out close, you may need to use 8 mm.