A couple of points.
Firstly, it's completely possible for a woman to transmit a claim without being eligible to be queen herself. Ever since Empress Maud failed to successfully claim the throne in the 12th century, this had been the working theory of English kingship, finally broken only in 1553. It's also the theory under which Edward III had claimed the French throne - if we're going by pure primogeniture, all of Philip IV's sons left surviving daughters, so Edward III's claim only makes sense as being the only *male* descendant of Philip IV.
This doesn't work out so well in 1553, because the only male descendant of Henry VII was Darnley, who's a small child and a Scot, to boot. However, if we expand ourselves to descendants of Richard, Duke of York, there's a lot more to work with.
First, there's the only living non-Tudor descendant of Edward IV, Edward Courtenay (b. 1527). His father, the Marquess of Exeter, a grandson of Edward IV and first cousin of Henry VIII, was executed as a traitor by Henry VIII, but he would later be restored to some of his father's titles and lands by Mary. He's reasonably attractive as a Protestant candidate: he apparently was partly implicated in Wyatt's Rebellion. A reasonably plausible candidate.
Next, there's a bunch of descendants of Clarence's daughter, Margaret Pole. Two of her younger sons still living in 1553 - Cardinal Pole, who would have been an attractive Catholic candidate in the absence of Mary (he'd specifically not been ordained as a priest so as to maintain potential eligibility), and Geoffrey, who was likewise a Catholic, and not very appealing as a candidate.
The heir of her eldest son, Lord Montague, was Lord Hastings, the future 3rd Earl of Huntingdon. He was about a year older than Edward VI, and was widely seen as a potential heir to the throne. Unlike his Pole relations, he was a Protestant, and a few years later, when Elizabeth seemed like she might die of smallpox, her ministers considered Huntingdon as a possible successor (since they certainly didn't want the Queen of Scots).
I'd say Courtenay and Hastings are your best bets for a male successor to Edward VI