Can I challenge a character with a '-' ability to a duel?
As per the rules reference, page 5, under "Dash (-)", the following bullet point is relevant (emphasis mine):


  
  A character with a dash skill value cannot be a challenger or challengee in a duel of that skill type. (see D.2 on page 23)
  


So, no, the character you describe cannot participate in a military duel, either as the challengee or the challenger.

The bullet point immediately above it covers the case where such a character's skill value is needed by an effect and that value is a dash (which can happen), in which case the skill value will always be 0 at the time it is checked by the effect and cannot be modified.