Congratulations and best wishes, Jennifer!
...anyone can officiate a wedding......setting up the paperwork in Inyo County would be best, since the county offices for Inyo County are in Independence, just up the road from Lone Pine.
By the way, another member here was married at Whitney Portal by mountain guide Kurt Wedberg. Getting married there might be much easier.
Yes, my wife and I were married at Whitney Portal by Kurt Wedberg in July 2007. You can get the process rolling at the Inyo County Courthouse in Independence (north of the holy city of Lone Pine). My family are not hikers, so my wife and I headed up to Lone Pine Lake (did not have permit).
Hope this helps.
Congratulations!