I think that Katori Shinto ryu is beautiful but as you say, It's not aikido. How do you reconcile your weapons training with your taijitsu?
I myself don' t practice TSKSR. But a lot of people around me do, because my aikido teacher also teaches it.
The swordwork we do is what Christian Tissier teaches, who was student of Inaba Minoru sensei. Plus we do some forms of aiki ken also.
But TSKSR inspires me a lot.
Mostly because it made me understand how important precise movements, postures and use of the body are. Precisely working on one's own body: This is very similar to what Endo sensei teaches. First tuning and building one's own body. Not relying on what uke does but creating connection or the relationsship from within ones own body.
And it teaches how "the ki things" can be learned on a bodily, down to earth way. No esotericism but just moving your shoulder a little bit here, your toe a little bit there - et voilà. This also relates to the teachings of Tissier: First work on your body, on your structure, on your correct movement.
So it is not certain forms or waza of TSKSR which are interesting to me. There is no maki uchi in aikido, the hanmi is different and so on. But the way of how to use one's body is interesting and helpfull to me.