Moist. It reminds me of mold and mildew--the things that grow in the cracks of dank cellars. Unfortunately, I’m not fond of “soggy,” either. That leaves me somewhat limited on terms describing mildly wet objects.
“Damp” isn’t so bad. But people get cranky when you describe their cakes as being “deliciously damp.”
“Dewy.” Now that’s a good word. “Dewy.”