Chinese skaters have the option of utilizing flights that pass through Russia as China is not subject to the same geopolitical restrictions on flights as the West. There's no need to worry about them.
Japanese and Korean skaters may take longer but could still get there. A cursory glance on flightradar24.com is showing some flights from Tokyo going from there to Paris, Stockholm, and Munich that are making a large arc to get to those destinations by flying above North America near the North Pole. (I'm presuming they would be able to make connecting flights to Tallinn through such major airports.) They also have the option of connecting with flights on Chinese carriers like I mentioned earlier. Again, I am not worried.