Dear RH,
Good day!!
Apologies for the inconvenience caused and please don’t worry, let’s work together on your concern and move towards a resolution path.
I understand your concern and to my knowledge, I would like to you know that when the content in the SharePoint Online site or OneDrive for Business has been shared to the external users (who are not part of our Office 365 organization) even with Edit permission, the external users will not be able to see the Open in the Desktop option for editing the shared file in the Office apps:

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Since the user having the problem is the external user that could be the possible reason for not having the option “Open in the Desktop” and I believe the shared Excel workbook can’t be opened in the Excel for the web directly because you mentioned the file size is too large. Reference: File size limits for workbooks in SharePoint - Microsoft Support
In this situation, if the user is having the Microsoft work account (******@companyname.onmicrosoft.com), you can add the user as a Guest user and place the Excel file inside a folder, and share the folder to the user. So, when the user access the shared folder, user can see the Sync button at the top, where user can click on the Sync button to view the shared content directly from the File Explorer and double-click on the Excel file will launch the Excel file in its respective Office apps.
Moreover, I agree with you having the ability to have Open in the desktop app option even on shared files for the external users will benefit the users and I suggest you to add your valuable idea as feedback in the SharePoint · Community (microsoft.com) which is the best place to share our ideas and improve the Microsoft products.
Appreciate your patience and understanding. Have a great day!!
Best Regards,
Sophia