Awesome- thanks, I'd missed that there was the option of different CSS for desktop & mobile. That's all working a treat now.
In case it should help someone else in the future, I did have to make a small change to the mobile CSS to get the icon positioned correctly:
.instaicon a {
background-image: url(/wp-content/themes/lay-child/images/Instagram-16x16-1.svg);
background-repeat: no-repeat;
background-position: 23px;
background-size: 20px;
}
Really appreciate your help :)