[Hunter]

Spoiler for Rasengan, Sharingan, etc.:

He said he made it as far as Yondaime which mean essentially the same thing.

I'm a bit unsure of the way Kakashi obtained the Rasengan to be honest.
Kakashi said that he wouldn't have created the Chidori if mixing Elemental and Shape Manipulation was so easy just before showing that he could use the Rasengan and explained he couldn't mix his Elemental affinity with it which implies that he tried to make an Elemental Rasengan like Yondaime, failled as well and thus created the Chidori. Since he created the Chidori before he obtained the Sharingan it would mean he learned the Rasengan without Sharingan.

But he also said he could copy this level of Rasengan and used the japanese word "copy" always and solely used for Sharingan copy. Solely until a couple of chapter ago when Juugo used it to speak about other people using the power of the CS. Still "transposed" power anyhow.
From this choice of word it would seem he did use the Sharingan or at least he can use the Sharingan for that.

So really I'm not sure, did he knew from Yondaime that mixing the Rasengan with an Element was virtually impossible which is why he created the Chidori and only later copied the Rasengan with his Sharingan?
Did he learn the Rasengan the regular way and only then the Chidori? In this case he could meant that with his level of Sharingan he can somehow copy/analyze a A-rank Shape Manipulation like the Rasengan but that's would be his max extent?
I'm not sure.

Anyway that's still Shape Manipulation so the user would have to be able to substain such high level chakra manipulation in the first place, Sharingan or not.