You could check the width of the user's browser window using JavaScript and then set the showThumbsButton and showThumbsOnLoad in the gallery's embedding code accordingly.
Create a sample gallery in JuiceboxBuilder-Pro and replace the gallery's 'index.html' file with the following code:
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<meta name="apple-mobile-web-app-capable" content="yes" />
<style type="text/css">
body {
margin: 0px;
}
</style>
<script type="text/javascript" src="jbcore/juicebox.js"></script>
<script type="text/javascript">
var windowWidth = window.innerWidth ? window.innerWidth : $(window).width();
var showThumbs = windowWidth >= 640;
new juicebox({
containerId: 'juicebox-container',
showThumbsButton: showThumbs,
showThumbsOnLoad: showThumbs
});
</script>
<title>Test</title>
</head>
<body>
<div id="juicebox-container"></div>
</body>
</html>