Saving to disk in mobi format without covers

[J Milford]

I have a Kindle Fire with limited space, so I would like to export from Calibre a large set of books without covers to save space.

I'm sure there's a way to do that with Calibre, but I couldn't figure it out from digging around here and Google. I don't want to change my covers in Calibre permanently, and ideally I wouldn't have to create a new mobi copy in the library itself (which is mostly epub), but instead just create the mobi copies as a Save to Disk output. I know there's the "Save to Format" plugin, but I can't figure out how to create a custom mobi output format without covers. But I know that doesn't mean it can't be done! I'm sure there's a way, I just can't figure it.

Even more ideal would be to export the books with small (20 KB, eg) thumbnail covers for browsing, but no big cover image when opening the book. But that's getting greedy -- just being able to export a large bunch of books without the bulky cover images would be great.

Thanks for any help! And apologies if this is in the wrong sub-forum.