Since gerrit 67468 it is possible to use [[Special:MIMESearch]] in miser mode.
It would be nice to have it also work for api. list=allimages has a aimime= param, but that is disabled in miser mode due to bad performance on the database.
You can also found some comments about the performance in gerrit 76954.
Created a bug to keep this in mind, maybe some days this is possible.