Can Trait Doctoring be used to change words like "nonblack"?
Yes, but not in your example.

A ruling on gatherer for Trait Doctoring clearly supports changing 'nonblack' to 'nonred'


  4/15/2013     The type-changing effect can change part of a word such as
  “nonblack” or “swampwalk” if the part of the word is being used to
  refer to a color or basic land type.


However, Trait Doctoring specifically says: 


  Change the text of target permanent by...


Doom blade is a not a permanent.

In order to change the color referenced on Doom Blade, you would need to use a card such as Sleight of Mind, that specifically says it can target spells. (See Steven Stadnicki's answer for more information about this combo)