I have two of the DMT credit card sharpeners. Don't worry at all about them bending or flexing. It's a hardened steel plate; thin but very rigid.
The 'hold' on these is something one needs to figure out, in their own way. When I use mine, I hold it with my thumb at one end, and my middle & ring fingers at the other. My index finger is folded underneath to support the hone from the back. I orient the blade diagonally downward, with my other hand, and sort of pull & draw the edge diagonally across the hone. I place the tip or pad of my index finger on the blade, usually near to the ricasso (sometimes on it). The index finger is what I rely upon, to keep the blade in flush contact, and monitor the feedback from the hone & edge.
I've been relying on a Fine (25 micron) and EF (9 micron) credit card so far. I use the Fine the most; it leaves a very good working edge. I've been tempted to get the Coarse as well. It would be advantageous for re-bevelling, especially with the small working surface area. These are continuous surface diamond, and the cut very fast for their size (as with all DMTs).
I have a small leather pocket notepad/folder, with credit card-sized pockets in either side of the leather cover. I tuck my hones in each of these pockets (in their plastic slipcases); it feels like a hard-bound book when closed. I carry it in my back pocket, with no worries about bending them.
