I have a similar issue, in desperate need of advice. I tried design2code's fix but that code is already correct.
I'm using the latest woocommerce version with latest rustik theme version and paypal. It's my first store and the launch is held up behind this one issue.
I'm not sure where the shipping option dropdown/radio buttons are supposed to appear but they display nowhere on the site. Ive tried dropdown and radio button options, no joy.
On the product page, no shipping options appear. On the cart page the default shipping displays with no option to change it (just text, no dropdowns etc). On the checkout page the shipping does change correctly according to the country selected from the dropdown on the address form.
I'm using the site with paypal so what i need is a very simple option to select either local or international shipping so as not to waste buyers time entering unneeded addresses etc. It could be either on the product, cart or checkout. I guess cart is best.