Can I give a creature First Strike in order to prevent it dealing any damage that combat?
Long story short, no: you can't give a creature First Strike after the first strike combat damage step in order to stop it dealing damage.  It will deal its damage as soon as it gets a reasonable window of opportunity.

Here's the relevant portions of the Comprehensive Rules:


  702.7b If at least one attacking or blocking creature has first strike or double strike (see rule 702.4) as the combat damage step begins,
  the only creatures that assign combat damage in that step are those
  with first strike or double strike. After that step, instead of
  proceeding to the end of combat step, the phase gets a second combat
  damage step. The only creatures that assign combat damage in that step
  are the remaining attackers and blockers that had neither first strike
  nor double strike as the first combat damage step began, as well as
  the remaining attackers and blockers that currently have double
  strike. After that step, the phase proceeds to the end of combat step.
  
  702.7c Giving first strike to a creature without it after combat damage has already been dealt in the first combat damage step won't
  prevent that creature from assigning combat damage in the second
  combat damage step. Removing first strike from a creature after it has
  already dealt combat damage in the first combat damage step won't
  allow it to also assign combat damage in the second combat damage step
  (unless the creature has double strike).