Two types of layout in woocommerce SHOP page [closed]

Set a button, or dropdown menu, that calls a function to set a cookie and to switch between CSS files which contain the _style ID:

function switchStyle(style) {
    var file = $TMPL_URL + '/css/' + style;
    jQuery('head').append('<link rel="stylesheet" href="' + file + '" type="text/css" />');
    jQuery.cookie($TMPL_NAME + '_style', style, {
        expires: 365,
        path: "https://wordpress.stackexchange.com/"
    });
}

jQuery.cookie should be replaced with whatever your standard cookie function is. Change expires: 365 to set whatever duration you wish, so the page remembers which setting was chosen for that user.