It’s never been explored, but that isn’t really a median for Supergirl either. The Surfer really doesn’t have to get into a brawl with her, nor does she have Wrath’s defenses against his power.
What makes you think that the battle ever has to become a slugfest? The Surfer can nullify her powers as surely as she is able to metabolize sunlight.
The Surfer brought a deer back to life, he used his power remotely without ever blasting or anything lot the sort, and yes he can remain intangible while doing so.
Kryptonian’s have DNA just like any other sentient race in a given universe, their bodies process sunlight differently than humans, but they still process it. The Surfer can change the way they do this. This has nothing to do with transmutation, he literally has the power to change the way that their bodies process energy, and just like the Hulk, and Lunatik, they have no natural defense against it.
Wrath had control of the most powerful creature in the universe in that book, and he was unable to even move. The Power Cosmic was destined to fail against him. Wrath is not Supergirl. She doesn’t possess his abilities.
However, if you want to argue that Kryptonian’s are immune to everything and possess no vulnerabilities, I’ll just agree to disagree.