Reply To: Removing cart from all pages/posts besides actual shop

Add this to Customize > Additional CSS:

.top-login,
.top-cart{
    display: none;
}

.woocommerce .top-login,
.woocommerce .top-cart,
.woocommerce-page .top-login,
.woocommerce-page .top-cart{
    display: inline-block;
}