You can force the checkout form to use a drop-down selector for the 'State/Province' and 'Country' fields by using the 'Condensed Form' option and adding those fields as an active custom field.

To enable this, select the 'Condense Fields on Secure Checkout Page' option on the Notifications/Custom Fields page of your offer.

With this option checked, the system will condense all fields into one block on the secure checkout page and will reduce the Billing Info fields to just card number and card expiration date. 

The first name, last name and address will be pulled from the custom fields. 

So with this option checked, you need to make sure that you capture any required address fields from within your custom fields that may be required for your merchant account processor.