Two questions which I need to ask:
a)who owns the devices?
b)what kinds of files are you sharing? You say, .mobi, but are you just repackaging .doc files or .pdfs into .mobi?
First, let's not use the word "side-load" because that usually refers to moving a file through USB. If you're "sending to Kindle", that obviously is not using USB.
I think what you're using is "Kindle Personal Documents service" to send it to a specific device.
The key question is whether your company owns the devices in question. If yes, then it also is controlled through a single Amazon account, in which case it would be fairly easy to delete and swap old Kindle files remotely.
To log in to the Kindle Personal Documents service via computer, go to the Amazon account options, choose "Manage your content and devices" , for show, select Docs . Under Actions choose Delete and that should do it.
I'm guessing that everyone owns their own device and use their personal Amazon login for it. I'm also assuming that each device has listed a specified employee's email as authorized to receive Kindle files from via the Personal Documents service. (Remember, the person may have several devices they are managing content on; they only need to authorize the device email which you want to send company docs to).
To add the file to devices for each employee, you would need to send a single email to all the relevant device emails and then attach the kindle file. Obviously if you can email one version of a file, you can email an updated version. If I send different versions of a file to a device, I usually rename the ebook's title (which is not the same as the name of the file).
If you don't have a single login for all devices (but are simply sending things from an authorized email to the devices), you do not have access to the user's Manage Your Content and Devices screen; therefore, you could not swap files.
To give a different perspective here, I prefer the Google Play Books solution for syncing ebooks to the Kindle solution. (For one thing, Google accepts epubs instead of a proprietary file). Google Play Books doesn't let different emails share files. But Google Docs/Drive is really good about allowing files to be synced and shared.
One solution might involve keeping the most recent epub/doc/pdf on a Google drive and let people manually transfer it to Google Play Books. (You could use a plugin like this: https://chrome.google.com/webstore/detail/drive-epub-pdf-book-to-go/fabbklgdcbijclhlffpmllpgnkalmbfd?hl=en-US ). But this still requires that each user make the manual step of connecting files from Google drive to Google Play Books.
If you can sync the file as a PDF or Word or ODT file, then you can stick the file onto your own G-drive (preferable in a separate EMPLOYEE DOCS shared folder), then each user could install the Google Docs/Drive app and then you could do a read only share with every user; that would let you always have a shared and synced copy of the file.
The only caveat about the Google solution is that might need employees to have offline access to these docs. I just checked and the Google Docs app has an option for each document which allows you to view the document offline. You would probably need to verify that Google would update a doc if an employee has chosen to make it viewable online.
(I suspect that MS Office might have a syncing method as well).
To summarize: Kindle doesn't seem to let you sync files among devices; it just lets you add new files. If the files you need to share can be PDFs/DOC files, then it would be easier to put them on the Google Drive and then share the files with users.