What is the altitude required to bypass Russia's airspace restrictions for airlines?
The Kármán line is considered to be the upper limit of airspace and the lower limit of outer space. According to the Outer Space Treaty of 1967 outer space cannot be appropriated by nations (nations cannot claim ownership of parts of outer space).

In that sense, one would be able to fully legally avoid navigation (and other) fees and bureaucracy imposed by any country one was to fly over if it was done above the Kármán line, but since the stunt would require a spacecraft, it hardly would pay off...