Thank you for your post. To answer your question, at the moment, there is not a way to order the csv column headers in the search export csv. As you probably already know, you can decide what the column headers are (i.e. what nodes are represented in the export csv) via the Arches Designer, but there is no way to determine the order. If others have experience with this, hopefully, they will chime in to this thread. I will say that if this is an enhancement that you would like any developer involved with Arches to be aware of, you may submit an enhancement issue to the Arches github repository (here's information on how to do that:
https://github.com/archesproject/arches/blob/master/CONTRIBUTING.md#issue). Also, if through your own Arches work, you are able to create a solution for this, please do share your findings with the rest of the Arches community through the forum.