It is permissible to handle one's clothes and dress himself immediately upon waking in the morning, even before washing his hands, though one who is stringent in this regard, and ensures to wash Netilat Yadayim before touching his clothing, is deserving of special blessing.
However, this applies only to one who went to sleep before Hasot (Halachic midnight). If one went to sleep after Hasot, then there is no reason whatsoever to avoid touching his clothes before Netilat Yadayim, not even as a measure of piety. The Kabbalists teach that the impurity which descends upon the hands while one sleeps arrives at the point of Hasot, and so if one went to sleep after that time, there is no concern at all.