OK, I'll try on this one.
I think the scenario you describe is not possible. Blowing up a volcano with
a bomb would be considerably less energetic than letting the volcano go off
naturally. In other words, large volcanic eruptions are much more likely to
produce the crack you describe than blowing a volcano up with a bomb.
Since such a crack has not yet formed (in billions of years of earth history)
the probability that it will occur is remote.
The real problem is that a volcano represents a weak (soft) spot in the
earth. A large earthquake - large enough to create such a crack would only
occur where a huge amount of strain had built up - something that is impossible
near volcanos because the heat allows the strain to be dissipated quickly.
If you look at mid-ocean ridge earthquakes, they are almost never larger
than Ms 7.0, never reaching Mw 8.0. The one exception might be an earthquake
in the Macquarie Ridge several years ago, but this was probably not volcanically
related, but part of the subduction zone.
The other thing that shows that there is really very little motion of the earth's
surface associated with volcanic earthquakes is that only one tsunamis has ever
been recorded associated with a mid-ocean ridge earthquake, and that was small
several years ago from the East Pacific Rise.
Consider the largest volcanic eruption of modern times - the eruption of Krakatoa
in Indonesia. It did create a large tidal wave, but once the eruption had occurred,
all that remained was a hole where the volcano had been - no cracks around the
earth, not even little ones.