1. The issue of difficulties of the sea voyage was raised from the first moment, by George V himself:
Lord Stamfordham, note of meeting - 9 March - Buckingham Palace
"I pointed out the King's apprehensions entailed in the sea voyage from Romanov (first name of Murmansk: Romanov na Murmane)."
Lord Stamfordham to A.J. Balfour - 17 March
"His Majesty cannot help doubting, not only on account of the dangers of the voyage, but on general grounds of expediency...."
The letter gives him away. What George V feared was not the Russian Imperial Family sinking with the ship and all hands in the North Sea. What he feared was they arriving safely in Britain. When the British government (who could and surely did consult the First Sea Lord, Sir John Jellicoe, about the matter) insisted in keeping their promise to the Russian Provisional Government, the strategy changed and Lord Stamfordham focused in the political consequences for the monarchy.
2. Kronstadt / Dardanelles.
Nobody at the time considered using Kronstadt as point of departure. The sailors of Kronstadt were a mutinous lot who had killed their officers and the sea voyage from Petrograd would involve passing by the German coast and going through the rattrap of the Danish Straits. The Imperial Family had to be picked up in Murmansk (Romanov na Murmane), on the Barents Sea (not the Baltic).
Dardanelles: It is not the right comparison. The whole Gallipoli operation was akin to storming a castle during the Middle Ages. The Turks, under German command, were waiting for the Brits and laid all the mines they could. Murmansk, on the other hand, was a harbour in an ally country, where British ships arrived frequently.
3. Murmansk (Romanov na Murmane)
Murmansk was one of the three ports used by the Allies to supply Russia with munitions during the war. The other two were Vladivostok, in the Far East and Archangel, on the White Sea. How busy were this ports? Norman Stone tell us in his book The Easter Front 1914-1917:
"There remained the ports of northern Russia, particularly Archangel, at the mouth of the river Dvina... As millions of tons of goods arrived in Archangel, the port became a scene of chaos. There were not enough wharved, warehouses, electric facilities, or even rails along which the boxes could be wheeled through the rudimentary streets of the town. The railway itself, with its capacity of twelve small train daily, could manage only a fifth of the minimum requeriment, 500 waggons...
This was still not enough - the more so as the blockage of Archangel was such that "mountains" of goods already existed to be transferred by rail at the turn of 1915-16. The government thought of developing an ice-free port: the Catherine Harbour at Alexandrovsk, subsequently known as Murmansk, offered reasonable possibilities for navigation all the year round, and the government picked up pre-war pland for construction of a railway between it and Petrozavodsk, on the way to the capital... Meanwhile, huge quantities of material built up both at Murmansk and Archangel: at Murmansk alone, 100,000 tons by March 1917...."
These "mountains of goods", "huge quantities of material" have arrived in British ships that followed the same route that the Imperial Family should have done in their way to Britain. They carried millions of tons of material, braving German submarines and mines. Those two dangers were not of the same order of magnitute. Sailors would have tell that they feared foremost submarines. The treath of submarines for the Imperial Family was done away with by the agreement with Wilhelm II. So it remained the secondary dangers of mines.
How big was the danger? I don't have statistics, but I would bet than less than 1% of the voyages between Britain and Murmansk (and back) ended with the ship sunk by a mine.
The "dangers of the sea voyage" were an excuse, a smoke-screen for the real worries (political) of George V and are now used by some posters as an excuse or a smoke-screen for his dishonourable behaviour towards his relatives, the Russian Imperial Family.