Congratulations and best wishes, Jennifer!
In California, I believe anyone can officiate a wedding. They just need to go to the clerk of the county where you are marrying, and do some paperwork. And of course they need to be responsible enough to file the paperwork once they return from the mountain. Telephoning the clerk of the county would help with this info.
Now it is an interesting question, what county is the Whitney Summit in? The crest of the Sierra is right at Mt Whitney, and that crest is also the border between Tulare County and Inyo County. Of course, I'd say 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. You might even talk some of your non-hiking friends into attending.
