I don't think that's really right... it's more the way you defined it, tbrod, than the way the urban dictionary does. I've often wondered how you say it but I guess it's as written - shaw with a slight p sound at the start
If the " Urban Dictionary is right , 'pshaw' has made a revival (and a change of use) since the late C17 ! Their version sounds quite insulting (and modern). The Shorter Oxford English Dictionary has it as "[ An interjection for ] Expressing contempt,impatience or disgust" It's pronounced as jno has it. By the C18 it was common as a dismissive utterance and certainly 'could be used by a female to put off or minimize a flattering comment or suggestion'
The words 'pish' and '****' were (and are) used to express disdain. I suspect that the Victorians considered these words too impolite to use in company, and so changed the pronounciation to 'pshaw'.
This was something the Victorians were renowned for. Thanks to them, the British bird originally called a 'whitearse' was renamed a 'wheatear'.