I don't know what you are talking about regarding a myth that the Japanese invented their swords. You've been reading the wrong books.
Any Japanese text makes full and clear reference to not only Chiense swords, but also spear and halberd (hoko and ko). The single edged straight sword was the norm through about the 8th or 9th century. Then the tachi- curved sword was developed. The question would be if the form of forging the curved sword is the same in China. I do not believe that it is - my understanding is that Chinese swords were made with a different forging process. And anyway, all that ends up with was if the Japanese, who clearly and openly acknowledge the 100% debt to China for their early weapons (excepting the bow), also copied the form of the curved sword, or came on that innovation independently, and then developed it in a manner consistent with the needs of the Japanese battlefield (China imported vast numbers of Japanese swords in the middle ages, considering them of far greater quality than their own). The naginata, (curved blade glaive) may also have been inspired or derived from Chinese weapons. The Japanese were certainly aware of the Chinese form, which are refered to as bisento, as early as the 14th century. The yari, or tanged spear, was developed largely in inspiration/imitation of the spears carried by Chinese and Korean warriors during the Mongol invasion.
As for other Chinese influences, Taoism, (yin-yang dynamism) is the esoteric basis in many ryu. The five element theory, in particular, pervades many ryu. Shingon Mikkyo - esoteric Buddhism - which was used to gather power, make incantations, etc., is, of course, derived from Chinese versions of Tibetan Buddhism. In short, the philosophical and esoteric bases of many of the ryu is China based. (Others are tied to folk Shinto, and the practices are far more geared to exorcism and ritual.
Ueshiba/aikido has no new techniques whatsoever - every one is in Daito-ryu, and forms of most of those can be found in a variety of jujutsu. As you can find most all of them in European texts from the 14th-15th century, I don't think it necessary to believe that the Japanese needed the Chinese to teach them TECHNIQUES. A lot of them were in sumo for over 1000 years. (Course maybe THAT came from Chinese/Korean/Mongol sources way back when). ANYWAY - I wouldn't be at all surprised if the more subtle uses of the body - the REAL tactics - are owed to the Chinese ----ki, kokyu, etc. For whatever my opinion is worth.