You can do better than radiation!
Moving ice by melting it with the radiation emitted from a decelerating Alcubierre bubble is like moving ice by melting it with the exhaust from your diesel excavator. You have a bent space bubble at your disposal! That will move your ice just fine.
The bent space created by an ALcubierre bubble scoops up photons as it "moves" and these are the ones shot out the front when the bubble decelerates. More detail here:
Using warp bubble of Alcubierre drive as a deflector shield?
In addition to photons, the bubble also scoops up mass in the way and shoots it out the same way. In typical space applications these are considered more or less cosmic rays - ions and atoms moving at near the speed of light and emitted along with the blueshifted photons.
The demolition applications of an Alcubierre bubble have not gotten the consideration they deserve. Ice is mass. I proposed that instead of pussyfooting around with some measley gamma rays, you drive your bubble down into the atmosphere and into the ice, stopping when you are in the other side. Atoms and molecules and pieces of ice which have entered your bubble of altered space will be scooped into the bubble and later emitted from the front into the underlying ocean.
The Alcubierre bubble compacts space which is how it achieves its end of "motion". Matter is a legitimate occupant of space. It gets compacted too as it enters the bubble. How exactly that effect changes the interface between compacted and noncompacted matter is an interesting thing to contemplate. People with such a drive will have some idea because they will be able to examine items that enter the bubble (are they still rocks? Atoms? Quarks?) and also these items when they exit the bubble.
I picture the part of the story where it is proposed that the ice be broken with particle beams and nukes. The Alcubierre engineer looks up from her 4d sudoku and waggles a hand dismissvely. "Nukes, schmukes," she says. "I'll break you some ice."