Blake's suggestion is definitely easiest, however you could certainly do some customization with Javascript and a hidden field if you wanted. Say your radio button has a CSS class "RadioBtn" and you make a hidden single line field with CSS class "HiddenField". You can then create the lookup rule based on the value in your hidden field, and use the following javascript to cause the radio button choice to be mirrored to the hidden field when you select something:

$(document).ready(function(){
	$('.RadioBtn input').on('change',function(){
		$('.HiddenField input').val($(this).val());
		$('.HiddenField input').trigger('change');
	});
});

The CSS to hide the single line field is just the usual

.HiddenField {display: none}