Don't have books here, so just some citations from aikido journal:
"Masakatsu Nakai 中井正勝
Middle school teacher in Sakai, Osaka. Teacher of Yagyu Shingan-ryu Jujutsu with whom Morihei UESHIBA studied ... "
"The technical content of this school is unknown but certainly included jujutsu techniques and the study of various weapons. Records are unclear as to whether Ueshiba's direct teacher was Masanosuke Tsuboi or Masakatsu NAKAI. "
"Receives Yagyu-ryu Jujutsu certificate ..."
I thought the question was "what influences of sword are present in aikido?" Nakai was reputedly schooled in Shinkage-ryu as well as Yagyu Shingan jujutsu -- and in my study I found that the koryu were never as categorically structured as the gendai arts. Lineages become less of concern after the late 19th century because there was much of both mixing and formal segregation going on.
I think it is fair to see Nakai -- and many others of similar or even less note roughly contemporaneous with Kano -- to be straddling that divide. Kano began the Kodokan before he even received Menkyo in Kito-ryu. Takeda may be viewed as doing the same thing for the aiki aspects of jujutsu leading to Ueshiba's work. Nakai may be viewed in the same general trend and began his own teaching a bare decade after Kano -- though clearly not remotely as influential. Ueshiba was at the latter phase of this process of a new syncretic and synthetic development in these Japanese arts. That categorical segregation between specific weapons work and between differing forms of empty hand work seems no small part of the genesis of gendai arts.
The Founder did acknowledge these studies as being somewhat formational in his tai jutsu -- and which certainly ought to inform our discussion on the topic of the training form for attacks in Aikido. Personally, I don't wonder about the presence of weapons movements in the aikido tai jutsu corpus -- they are now readily apparent to me -- highly applicable -- and easily demonstrable.
I have other --more concrete -- thoughts on the relationship and developments of and from weapons to aiki, but that would be beyond the point of your post.