Margaret, the elder sister, marries King James of Scots as per OTL.
Elizabeth would no doubt be employed as a marriage pawn on the continent, with the purpose of securing international recognition of Henry's title to the crown. The Tudors were eager to connect themselves with the Trastamara and Habsburg alliance at any cost - Henry VII courted both Juana la Loca and Joanna of Naples while Henry VIII was betrothed to both Catherine of Aragon and Eleanor of Austria. So I can see Henry advancing Elizabeth as a bride for Ferdinand following the deaths of Arthur and Isabella which imperiled the Anglo-Spanish alliance and devalued Catherine of Aragón as a prospective bride. If Ferdinand turned her down, Christian II of Denmark (four years older) would make the most respectable match out of all the available bachelors. Failing that John Stewart, Duke of Albany (heir to Scottish throne), Gaston of Foix, Duke of Nemours (the only nephew of King Louis XII) or Anthony, Duke of Lorraine and Bar (whose family claimed the crowns of Naples, Jerusalem and Aragon) would make more or less suitable matches. Unfortunately for her father's policy she would be far too old to be seriously considered as a bride for young Charles of Castille.
EDIT: Considering Henry VII hated spending money, he'd also consider that when it came to choosing a bride groom. A son-in-law of lower rank might make less demands than a King. Some financial deal where unpaid parts of Catherine of Aragon's dowry got factored into Elizabeth's dowry (for a Spanish match) or where arrears of Henry's own French pensions were abated as a dowry for a French match (basically transferring King Louis' debt to Henry to the bride-groom, in this case his nephew) might be of interest.