Can I replace only the smallest cog on my rear cassette?
You can replace the smallest cogs on cassette.
For example see Sheldon Brown's Building custom cassette page.


  For example, Shimano doesn't make any true "corncob" (one-tooth-jump)
  cassettes for time-trialists or flatland riders. In 7 speed, the
  closest is the J (13/14/15/16/17/19/21).
  
  If you remove the 21-tooth sprocket from a J, you can make it into a
  13-19 corncob by buying an 18 to put between the 17 and the 19.
  Alternately, you could make it into a 12-18 by removing the 19 and the
  21, and adding a 12 and an 18.


There is also about MTB &amp; Road compatibility:


  "Road" vs "Mountain" Hubs There is no interchangeability issue between
  "Road" vs "Mountain" cassettes and hubs as long as the number of
  sprockets matches. Although "Road" and "Mountain" hubs are no
  different as far as cassette fitting is concerned, they are different
  in terms of overall spacing. "Road" hubs generally use 130 mm spacing,
  while "mountain" hubs are 135 mm.
  
  "Mountain" hubs will likely be slightly better sealed against dirt and
  mud than "road" hubs, but this is rarely an issue in practice. The
  wider 135 mm spacing will generally result in a slightly stronger
  wheel due to reduced dishing of the spokes.