Q: Can I change the order of the first two authors in an article with shared authorship?

Any change in authorship or the order of authors is supposed to be made before the article is accepted for publication with the consent of all the co-authors. Moreover, it is odd that you would want to change the order of only the first two authors and make it alphabetical. If you and your co-authors have agreed to using an alphabetical order of authors, all the co-authors' names should be in that order and not just the first two. However if you have discussed this change with your co-authors and they have agreed to it, then you can go ahead and make the change. However, note that it would be unethical to make the change without the consent of all the co-authors. 

While submitting your revised manuscript, you can make the change on the Title Page and explain in your Cover Letter the reason for revising the author order. You should explain that all the co-authors have agreed to this change. You would need to either get this letter signed by your co-authors or should copy them on the email that you send to the journal editor. Once you have done this, the journal editor should be able to accommodate your request and update the author order. In addition, you must also update the author order in your online journal submission system.

Related reading:

• Can I change the first author of my journal article after submission?
• Can the corresponding authors and order of authors be changed in the revised paper?