Temporary removal of one load bearing stud
One missing common stud is unlikely to cause problems, but the best answer is to observe what happens when you remove it. Is it very tight between the plates? Do you hear any creaking or popping from above? Does anything settle visibly or by careful measurement? 

One other approach would be to install a small header (a 2x4 U would do) between the adjacent studs and tight to the top plate, and support it with trimmers tight to those studs. That would leave you with a 28-1/2" space in which to work and more confidence in a successful result. When you no longer need access, simply install a stud below the header in the original location.