It should be noted that the Catholic church is against the death penalty.
In most cases, yes it is ... however, support of the death penalty in general does not run counter to Catholicism.
...likely the second least painful method of execution ever invented ... especially with modern-age squeamishness disliking the fountains of blood associated with the Guillotine ...
So the Guillotine is the least painful method of execution?
Although the head "lives" for about seven seconds before the brain is totally deprived of blood and oxygen; hence why the French would hold them up for the crowd -- so the victim could view his audience.