To the best of my knowledge there is only one person on the planet who has a listing of everyone who served in the Crimean War and no one has been able to make contact with him in the last three or so years. Absent that, you would need a bit more information to begin a search, such as the regiment he allegedly served in. Armed with that information, I am sure someone here could advise on how to proceed.
Based upon his date of birth I would guess that he did not see service in the Crimea, as there were few people below the age of 17 who served there . . . although there were a few as young as 15 I believe, so he is not completely ruled out.