A few years back we practised a bit with a short sword. It was a dual wielding practise with a short sword (wakizashi) in the left hand and a normal sword in the right.
There are some sword arts (kenjutsu) that practise this (this for example), but I think it is uncommon in aikido.
In the 5 years that I've been training, there were only two lessons where we used the short sword. And then still we used in in combination with a normal length sword.
I did buy a matching set of a short and long sword, just because I liked it.

That E-Bogu lists them under their aikido section does not mean it is used a lot in aikido. I also see they list shinai under aikido. But that is a weapon used in kendo and it's not commonly used in aikido.
I think E-Bogu is just not very accurate in the categorization of their products,