Time Sweeper handedness

I recently got into a conversation about the existence of left-handed Time Sweepers.  We never see a left-handed sweeper model (with a single exception of a character's sweeper becoming mirrored for a single shot, which is clearly a mistake by the devs), but we see four of the six recognized characters (everyone but Blinx and Chron) use their sweeper left-handed at least once.  One character, the unnamed cat with a green hat, even seems to prefer his left side, using it more often than the right.  This led to some thoughts and eventually this little sketch to act as a visual aid.

The sweepers clearly seem designed for a right-handed user, given how the clock only faces outward if held in the right hand.  It turns out that there are some other issues with wielding one left-handed as well, such as holstering it on the back of the user and retrieving it quickly, as the way it's normally holstered results in the handle appearing on the right side, not the left.  This is solved by rotating the sweeper 180º, resulting in the handle being on the left instead (making both holstering and drawing possible).  One final issue appears, though: if a left-handed user reaches over the shoulder to grab the rotated sweeper, they'll end up holding its handle backwards with the barrel facing behind instead of in front.  This requires the user to reach under the shoulder instead of over it, which is arguably more convenient in the first place.

I propose that Green Hat be depicted as left-handed and wielding his sweeper in the manner described above.  Seeing as how we see Green Hat shoot left-handed more often than not, and this seems like the only reasonable way to wield a sweeper in such a manner, it doesn't sound like any stretch of canon.

The Time Factory logo is stupidly complicated and annoying to draw at such a small size, by the way.

Fuck me I forgot to draw the bell in one of these