I don't know when Sheaffer started making the squeezy converters; that is something I'm curious about also.

But I do know that they fit into the old student market "Sheaffer Cartridge Pens", including the original rounded end versions which initially were called Skripserts. I have about 20 of these (maybe closer to 30) and use them frequently. I've fitted the old Imperial/Targa squeezy converters in them with no problem. They don't fit into the student market pens that have the shrouded nibs and are now most commonly called "Skripserts" online and were called Skripserts in advertising copy after the original open nib cartridge pens stopped being called that. Or rather, they "fit" into the shrouded nib pens but get easily stuck in the barrel. This, despite that these pens have a larger outside diameter than the "Cartridge Pens". It is possible they were meant to fit but my pens' plastic has shrunk just a tiny bit over the years and that causes the converters to stick in the barrel.

The current piston converter does not fit into the original open nib student market Cartridge Pens/Skripserts, which I'm sure is not new information to the collectors discussing things in this item, but FYI for anyone else reading this. Only the old squeezy converters fit.

There is at least one Imperial that takes carts but has a short barrel; it doesn't have the void at the end of the barrel past the shoulder that stops the end of the cartridge, and that void is needed for the squeezy converter to fit. This is why that Imperial is "cartridge only" and not C/C. I have one of these, unused NOS with case and original box of carts and everything (purchased a couple years ago from Peyton St).

Given my experience with those two, it would not surprise me if the old converters don't fit some or all the Lady cartridge pens/Skripserts, but I don't have any of them so no experience or testing.