Asking Chewie to cook would probably be the smart move. Han would, hypothetically, be willing to cook for her, but there's no guarantee it would be much better than what they've got in storage. He has a great many skills, and will claim even more than he's got, but a gourmet he definitely isn't. (Still, he'll admit, this is no way to woo a princess. Somehow it's worked out in spite of that.)

He's being slow and gentle as he can, but that... well, is not the sort of reaction he's aiming for, obviously. Though he supposes it could go worse. Still, they can do better than that. He nips idly at the corner of her jaw, shifts a little to aim for a better angle, and moves again, being a little less tentative about it.