It could be done, but to be honest, it won’t be easy to make it smaller like 960px, such as the example site you listed. There would be quite a bit of CSS adjustments to the responsiveness of the theme that would be required, and it looks like the menu needs some adjustments too.
There is a setting though in the customizer under “Site Settings” that gives you a preset of page widths you can use, although this gives you a boxed style. The Boxed 1200px Width setting would give you something close to that, but again, this would be a boxed style. You could use this and then change the page background to something different.
But, if you still want to try out modifying the header sizing, you can give this a try:
#masthead .container {
width: 100%;
padding: 0 30%;
}
It does start to get a bit distorted though on smaller mobile screens.