So, in regards to this, would we see Henry VII being married to one of York's daughters or would he be pushed for a foreign marriage?
Depends on how stable York thinks the Regency is. If he's in control, and Margaret's gone off remarried somewhere out of England, and he's raising the King, I can see him aiming for a foreign match. Some matches that may occur, in order of likelihood:
Eleanor of Naples: A solid foreign match that would provide a decent, dependable alliance. Not the greatest royal match, but considering Henry VII's mother is the second daughter of a Duke, the eldest daughter of a King is a step up.
Maria or
Bona of Savoy: A match with Bona was in the works of Edward IV of England OTL, so I can see a match with Savoy being suggested ITL for Henry VII of England, particularly with similar people around him. Hell, I would even suggest a double match might occur, with Henry marrying one of the Savoy girls, and Anne or Margaret of York to Amadeus IX, Duke of Savoy.
Margaret of York: The youngest daughter of the Regent, he may, if a foreign match seems unlikely or without gain for himself, aim to have his daughter who is nearest in age to the King marry him.
Magdalena of France: This might occur if Richard of York, as Regent of England, makes some considerable gains in France, and demands a French Princess for the King. If this occurs, then the match would probably be done to celebrate the success of the French campaign.