WI: Edward of Westminster had been born a girl instead?

As the tin says, what if Henry VI and Margaret of Anjou had had only a daughter, Catherine, in 1453 instead of OTL's Edward of Westminster? Would the Yorkists have attempted to capture and marry her to their own?
 
Margaret of Anjou is in a weaker position, without the birth of a male heir. Does this at all inhibit her ability to rally supporters? Conversely, without her birthing a male heir (whom York needs to dispose of if he wants the throne), her opponents might be less inclined to accuse her of cuckolding the king?

I'd imagine a match between her and Edward Earl of March (IOTL Edward IV) would get thrown around a lot in the late 1450s as some kind of compromise, despite the age difference. Though that's unlikely to satisfy anyone.
 
I think Margaret of Anjou would be troubled in seeking a match for her daughter - the man would need to be strong but relatively without supporters if Catherine was to hold much power. If a York was to marry her, it would give them a very strong claim to the throne as King Consort and most likely they would take over completely. The War of the Roses would possibly be less bloody if Catherine was married to Edward IV, as the Lancasters and Yorks could possibly unite under any male heir born to them (think the Tudors, with Elizabeth of York and Henry VII). Alternately this could breed more conflict within the Yorkist faction, with George of Clarence possibly still wanting power for himself. It would likely depend on if/when the marriage between Catherine and Edward IV took place and how quickly a male heir was produced, as well as how much influence Margaret of Anjou had over the couple.
 
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