If as is likely the boy is a Protestant Edward VI's names - Edward/Henry Grey is named in his device for the succession - and events unfold rather as they did in OTL - the reality was that excluding Mary and Elizabeth was in most people's eyes not right - they were legitimacy issues aside the daughter's of a King and were being displaced by someone who was not. Mary was still relatively popular and had a lot of support.
Now if the boy was the first child (born sometime between the marriage of Frances and Henry in 1533 ish and the birth of Jane in 37) then the obvious solution was to marry him to Elizabeth - which Edward VI might well support - his favourite sister would not be Queen Regnant but it would give the couple's children a unified claim and might be enough to garner support - again there is every chance that would not have happened before Edward's death though