Changing Site Header Button Font

Hi all!

I am working with someone's website that did start from a template they purchased and I'm just looking to update all their fonts and colours to match their current branding. I've changed the default font for the buttons globally across the site, and have also successfully changed the font of the site header text as well, but the site header button I just cannot figure out how to get to listen!
The website is https://www.handleandhone.com/

.header-nav-item a {
  font-family: 'Avenir Light' !important;
} 

Worked for the header text but not the button, and there is some code in the custom CSS from I think the template she purchased and I don't know if that's effecting things at all... 

//FIXED HEADER NO BACKGROUND//

.header
{background-color: rgba(0, 0, 0, 0)!important;}

thank you thank you thank you thank you!!! @Lesum