Yes and no and yes.
Yes, you could use Sigil to copy the CSS files from one ePub to another.
No, that won't help, because the effect that the CSS has on the layout depends on how CSS is used in the HTML.
Of course, if you're prepared to also edit the use of the CSS in the HTML (using Sigil) you could. But you might not consider it to be worth the effort.
I'd recommend looking at calibre's options for conversion to ePub. They also work on converting ePub -> ePub to re-write some of the styling.
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