If you have the favourite weapon, you also have to have the least favourite weapon...
Perhaps create a stats file that's updated every runthrough of the game, with favourite and least favourite weapons and the rest of that autism for both that game, and for the entirety of what's in that file.
All your least favourite weapons are the ones you haven't picked up yet. It wouldn't be a very interesting statistic.
We don't track stats across multiple plays, for a number of reasons - there's no concept of a user in sphereFACE and lifetime statistics wouldn't be very meaningful for games shared by multiple players, different tactics and so on.
A once-per-lifetime least-favourite list of anything is going to be a long list, since in a typical single run of the game the player won't encounter most game features.
And I'm sure that rather a few players would appreciate the ability to gauge how their gameplay styles have changed over time, being able to look at analyses of pure information rather than looking back at the visually-apparent aspects of their playing.
If you'd just like a file dump of the stats displayed on death, that can be arranged - those are basically all the stats there are. And a least favourite weapon of all those picked up could be added, but it's again possible for it to be half a dozen different weapons you've picked up and never fired each game, so I'm not sure how useful it would really be. You'd still need to track your stats file's changes manually...