If earthquakes don't trigger volcanoes, probably nuclear explosions would not either.
However even large earthquakes that release incredible amounts of
energy and can rupture very near volcanoes have not triggered
eruptions. This happened just recently with the 16 April 2016 Kumamoto
earthquake and nearby volcano Mount Aso. Despite being an active
volcano and a mere ~30km or so from the earthquake hypocenter, the
eruptive activity did not change in character after the seismic waves
passed through it. We'd certainly learn a lot if someone did go and
inject a bunch of fluid into a volcanic area, just as we have learned
loads of science from the experiment being done in Oklahoma.
Mud volcanoes are not Krakatoa caliber things but still pretty awesome.
The Sidoarjo mud volcano was supposedly started by people doing fracking. If fracking could do it I bet a nuclear explosion could do it too. I suspect that the difference is that the mud is not as deep subsurface as lava is.
I am not sure what the difference is between a mud volcano like Sidoarjo and a volcanic lahar: definitely a volcano, also mud, super destructive.
Large lahars hundreds of metres wide and tens of metres deep can flow
several tens of metres per second (22 mph or more): much too fast for
people to outrun. With the potential to flow at speeds up to 100
kilometres per hour (60 mph), and flow distances of more than 300
kilometres (190 mi), a lahar can cause catastrophic destruction in its