Great, thanks, Tom. That worked perfectly.
Anyone looking for this, this is what I used to have the SHOP page have a no sidebar with all other shop archives set to have a sidebar (which you need to set in your theme settings):
add_filter( 'generate_sidebar_layout','tu_custom_woocommerce_sidebar_layout' );
function tu_custom_woocommerce_sidebar_layout( $layout )
{
// If we are on a woocommerce page, set the sidebar
if ( function_exists( 'is_woocommerce' ) && is_shop() )
return 'no-sidebar';
// Or else, set the regular layout
return $layout;
}