Can you perform a log transformation, i.e. Log2 on your 2^-DDCT data to reduce the skew, thereby performing parametric tests as these may be more robust and reliable than non-parametric tests.
No. ddCt-values can be negative, and logarithms of negative values are not defined. If the (frequency) distribution of ddCt values really shows considerable skew, you are missing something in your model like missing then consideration of an important confounder, factor or interaction, or your assay hat a problem (unspecific amplification, used Ct values are not in the linear range (LoQ) of the assay, etc.). Think about this first before you think about torturing your data.
As ever with these things, I would advise you to look at your primary data very carefully. The danger in using ddCt is that you're looking at a number derived from a derivation of your primary data (losing information at each step), and when your primary data is effectively log transformed already, it is incredibly easy to lose track of what you're doing, and what the numbers mean.
So before doing anything else (let alone what you're proposing, which you should not do) I would suggest you double check all your Cq values to make sure you can actually trust your ddCt values: make sure all your reference gene values are comparable, and you don't have wild variation in cDNA between samples -this is a common source of skew-, make sure your reference genes are well validated and are not showing any obvious treatment-correlated changes, and make sure all your Cq values are trustworthy: you don't provide any raw data, but in my experience values above ~28 are increasingly prone to well-to-well variation.