any ways there's no guaranty that Olga would be a carrier of hemophilia, and if she was it'd hardly be the crisis that rocked the Russian monarchy, for one the Monarch of the UK in 1914 didn't rule, he reigned, while he had great influence and some power in foreign policy, he's not the Tsar and Autocrat, so a sick king is a personal, not a political issue, leaving that aside, while in the sexist 1910s a male heir would be strongly preferred, its hardly required by the UK constitution, farther more if some how Edward and Olga had no children, unlike Nicholas II Edward was A) not yet the monarch, and B) had 3 (well 4 but lets not) brothers all of whom would be married in OTL before the death of George V Nicholas II had one dead brother and one brother in exile for his unsuitable marriage leaving no popularly known heir outside his children, also C) unlike Nicholas II Prince Edward's sister could be an heir
so A) there's no way to know if Olga was a carrier of hemophilia, B) even if their son(s) did have it, hardly a national crisis C) if all their sons die from hemophilia(or they had none) daughters can and would become Queen, again hardly a crisis, D) Edward's brothers are well known and popular there would be little popular shock if one of them become King, in OTL Edward was unmarried at age 42 it was understood that his brother Prince Albert (or failing that the Princess Elizabeth) would be the heir on Edward's death him being single and childless in OTL wasn't seen as a crisis
Ok. If your absolutely sure. I mean you've really thought through a sensible situation here.
I suppose George V and Queen Mary would be really excited at the prospect. I mean their close relations, the Tsarina Alexandra, Queen Ena and Princess Alice of Albany and their husbands had amazingly happy lives watching their children struggle with a life threatening illness, why wouldn't any sensible parent wish that situation on their own son? Its not as if the son and heir would be expected to carry out long, extended Imperial tours or train in the military as George V and his elder brother or his sons had done.
It was widely known within the family that the Tsarina Alexandra was a carrier of haemophilia, it was known that at least 1 (Princess Irene of Prussia) of her 3 sisters were also carriers. Of Irene's three sons, two had the condition.
Of the 4 daughters to reach adulthood of Grand Duchess Alice of Hesse, 2 were defintely carriers, Elizabeth never had children so its impossible to be clear.
Still those are not great odds.
Its interesting, at the same time you are proposing that King George and Queen Mary would let/encourage their eldest son and heir marry a bride, who had the potential to destroy the British blood line, they had their own little problem.
Prince John.
The way they dealt with that is quite interesting and rather telling. He was separated from his family and sent to live in semi seculsion. His condition was kept secret from the public out of fear it could be seen as damaging.
King George and Queen Mary clearly had a great deal of sympathy for children, who were born with disabilities.