No, the checkbox and radio button are very well established user interface elements, to swap them would be akin to swapping the brake and the accelerator in the car (though not with as dire consequences).
If your art director thinks they are ugly you could contrive something with JavaScript and CSS which functioned like either but looked much prettier than either checkboxes or radio buttons. You can then use hidden form fields that are also updated on click to provide the form submit data that you will require.
But please don't make a radio button look like a checkbox, just make a prettier radio button, and, make sure you've covered everything that a radio button can do (i.e. the ways it can be checked).
This is not particularly tricky mark-up or JavaScript and would leave you with unconfused users and a happier work relationship as both your requirements would be satisfied.