'rather than any...of skill.'
The word that comes after 'any' in this sentence must be a noun: 'any (something) of skill'
'lack' is a noun. 'shortness' is a noun; but 'short' is mainly an adjective, and also an adverb.
This rules out even a consideration of 'shortness' as a possibility, since it is not listed as an option.
Student or Learner