It will but the tools will be loose :/. Standard brass rod works at 3/32 but you will need to file/sand it down.
[Begin rant]: Why can't Victorinox just use a commonly-available size of rod for all of their pins? The backside tools already have 2.5mm holes, so their 2.25mm pins are undersized to begin with! [End rant].
I decided not to use the 2mm stock for pins in my latest SAK mod. Instead, I ground down 2.5mm stock by spinning it by hand against the bench grinder wheel, then sanded it smooth. It actually worked really well and was much faster than trying to reduce the diameter with sandpaper alone.
It’s too much work to do by hand alone! I only turn pins when I need nickel silver, since I can’t find a source. But there are a few ways to get brass rod in 2.2mm at reasonable prices.
To be clear, what I mean is that I hold the 2.5mm rod against the spinning grinder wheel and turn the rod between my fingers as I move it back and forth. This method does leave a slightly uneven surface, but some quick sanding with medium grit paper evens out the surface to a level that I find acceptable. It's not a perfect method by any means, but it was good enough to build this: