RF Cautery DNA damage?
The thing about DNA is that it's very durable, compared to the rest of the cell. It's not too difficult to extract DNA from cooked and processed food, even though the definition of "cooked" is "denatured and broken many of the proteins in the cell". The long DNA strands may be broken into long pieces, but overall the DNA holds up very well to heat. There's no risk of DNA damage to neighboring regions with RF radiation because the primary way RF energy destroys DNA is through heating, and at the temperatures where DNA starts to accumulate damage the cell around it is cooked/destroyed.

The quantum explanation for why ionizing radiation can destroy DNA is that high-frequency radiation is powerful enough to zip through the surrounding tissue and break/damage individual DNA molecules. Individual radio photons can't "gang up" on a DNA strand to do the same thing because of how quantum mechanics works, so you won't be able to break the strand or damage the bases without high-energy ionizing radiation.

Metaphorically speaking it's like trying to get at a peach pit. Ionizing radiation is like a knife, it zips through the flesh and can get at a peach pit without damaging the peach much. RF radiation is like a belt sander. You can definitely get at the peach pit, but you'll cause a lot of collateral damage doing it.

Mutations or DNA damage that might cause cancer can only happen to cells that are alive that receive DNA damage. If the DNA is damaged by heat, the cell around it is dead, and that DNA damage doesn't really matter.

I encourage you to read about ionizing radiation and the photoelectric effect.