The other charge relates to failing to notify Maritime New Zealand of the incident as soon as possible, which carries a maximum fine of $5000.
Henderson, an Invercargill resident who is still employed as one of three masters of the Santa Regina, was excused from appearing in Wellington District Court today.
He indicated through his lawyer that he would elect trial by jury on the first charge, with the second charge to be set aside until the trial's conclusion.
Henderson could not previously be named while he sought name suppression, but APNZ today learned a stay on publishing his name has since been lifted.
His former lawyer Anita Miller had argued in January that naming Henderson would tar him with the brush of the Costa Concordia disaster.
The Costa Concordia's captain, Francesco Schettino, is facing multiple charges after the cruise ship ran aground off the coast of Italy in January, leading to the deaths of at least 17 people.
Schettino has been criticised for apparently abandoning ship before everyone else was safely off the vessel, and for refusing to return to oversee the evacuation.
Ms Miller argued revealing Henderson's name would adversely impact on his professional reputation.
He could also suffer a loss of income from the potential loss of contract work.
Henderson was master of the Santa Regina for roughly half the year, but the rest of his income came from contract work for various other companies.
Ms Miller said Henderson had an exemplary record, with no previous incidents to his name throughout his 48-year career.
Henderson will be represented at trial by Michael Reed QC, who was David Bain's defence lawyer, and experienced maritime lawyer John Burton.
The Santa Regina's operator, Strait Shipping, is also facing two charges under the Health and Safety Act. It denies the charges.
The charges were laid after Maritime New Zealand carried out an investigation into the incident last year.