Crossword Genius

River to cross with some style, one fancies (4)

Ross

I believe the answer is:

styx

I'm a little stuck... Click here to teach me more about this clue!

'river' is the definition.
(mythical river)

'cross with some style one fancies' is the wordplay.
I cannot really understand how this works, but
'cross' could be 'x' (an X is a cross) and 'x' is found in the answer.
The remaining letters 'sty' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...

'to' acts as a link.

Can you help me to learn more?

(Other definitions for styx that I've seen before include "River crossed at death" , "Mythological river in Hades" , "River Charon rowed on" , "'River of Hate' in Hades" , "classical stream" .)

I've seen this clue in the Evening Standard.
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