Separating the rivet sounds plausible, but I have only drilled and that works. Clamp in vise to drift the center pin, it is snug. Plan to use new pin material to replace.
There are of course 2 different 2138 models. The old pre 90 has a thicker blade and spring, making the handle wider, it is more robust than the newer post 90. The late models have a deeper blade belly and more narrow spine and spring, not as hefty but a better kitchen slicer, akin to a substantial paring knife. My first disassembly was an old model in pristine condition but a very weak spring. Case would not fix it, so I decided to take it apart. I surmised that it must've spent its life half opened in a display case.
The old models have a rear pin that is captive in the spring, but newer design pin is not captive and the spring lifts out with only the center pin removed. It is not necessary to replace the pivot when performing the spring re-arch.
As Obsessed mentioned, Vise is best way to tighten the existing cutler rivet.
If replaceing pivot, old models need a 1/2 long barrel, new models need a 3/8 long barrel. The pivot screws will sit nicely down in the pre-existing scale countersinks.