I've been considering what I should do in those rare cases, more frequent in summer, that a pair of shorts does not have a 5th pocket to carry around a MiniChamp and light in, but the main pockets are out of bounds.
I had found a small Victorinox pouch (4.0518.XL) years ago, and it turns out that one of the Olight 3E Eos' I bought recently is small enough to be able to share the space inside it with an Alox MiniChamp, with a little bit of room to spare.
Also, I have some dislike for unthreading and rethreading belts from shorts just to attach a pouch, so I proceeded to blind-rivet a belt clip to it.
The result is a very small, quick to attach EDC option. I used some of the spare room for a piece of shrink tube lodging tweezers, toothpick and MiniChamp pen as those won't fit in my Alox MiniChamp, but a normal MiniChamp with these integrated will also fit.