You can 'pay cash', or 'pay in cash', or 'pay with cash' but not 'pay by cash'. You can 'pay by cheque' though, so it would sound better to say, "You can pay by cheque or cash."
In your last, the word "by" transfers to "cash" also. If you really object to "pay by cash", then it would be better to say: "You can pay cash or by cheque/check."
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