Given this is an extremely unlikely scenario, let's have som fun with it.
Now, the only people who've called themselves Dukes of Estonia the last 200 years or so by 1900 are the Romanovs, since Estonia is probably getting independence from Russia, it's unlikely they choose a Romanov prince. Could perhaps work if they are content with being a vassal state of Russia, but unlikely.
Now, except for the Russian Tsars, only two European royal families have claimed the title "Duke of Estonia", Sweden and Denmark. Sweden officially abolished the title in the 17th century, and they have since changed ruling dynasty completely. Denmark never technically gave up their claim to the Duchy and sporadically used the title even after they lost all of Estonia in 1346. So maybe a Danish prince?
How about Prince Valdemar?
Not only a smashing good looking fellow, but also the only of Christian IX's children that isn't/has been either the ruler or consort of a foreign country. He is also named Valdemar, which is the same name as the Danish King which conquered Estonia in the 13th century, receiving the Dannebrog flag near modern Tallin, where it's also the city's symbol. Why not make him King/Duke?
Again, not at all realistic, but perhaps a bit fun.