"That kind of thing stays in the back of your mind during the whole cruise," Spector said. "You're always thinking, 'Well, chances are nothing's going to happen, but if it does I'm going down with the ship, I guess.' "
Frederick, the cruise line's lawyer, called Spector's allegations "categorically false." The company says the ship Spector sailed on is one of its older vessels and is being phased out later this year.
The company has equipped its newer ships with a range of amenities for the disabled -- from grab rails in the bathroom and flush walkways into rooms and showers to adjustable clothing racks in the closets that lower to a wheelchair-user's level. Around the ship are handicapped-accessible public restrooms and room in the ships' casinos and entertainments theaters for wheelchairs.
Norwegian Cruise Line president and chief executive officer Colin Veitch told ABC News that the modern fleet has been designed with the needs of travelers with disabilities in mind.
"We have removed every barrier that's reasonable to remove without compromising the safety of the ship," Veitch said.
Veitch also said the company is providing special training to its crews on how to cater to disabled passengers.
"Our aim is to make sure everyone has a fantastic vacation," Veitch said. "And part of the training that our crew go through is to sensitize them to the special needs of passengers with physical disabilities."
Spector says he is not seeking money or compensation from Norwegian Cruise Line. He says he just hopes his case will bring change.
"Hopefully, through what I'm doing, it will help people in the future that are disabled, that they won't have to encounter the same things that I did," he said.