I think this is probably Hot Sky at Midnight by Robert Silverberg. It was published in 1994 so that fits with the time you remember reading it.
The character with no eyes is Farkas. In a conversation he explains:
“And you were born like this?”
“Some kind of genetic accident?”
“Not an accident,” Farkas said quietly. “I was an experiment. A master gene-splicer worked me over in my mother’s womb.”
And as you say only people without sight can operate the FTL drive:
The faster-than-light field distorts vision,” Farkas went on. He didn’t appear to notice that she was standing and looked about ready to bolt. “It disrupts vision entirely, in fact. Perception becomes totally abnormal. A crew with normal vision wouldn’t be able to function in any way. But it turns out that someone with blindsight can adapt fairly easily to the peculiar changes that the field induces. As you see, I would be ideally fitted for a voyage aboard such a vessel, and indeed I have been asked to take part in the first experimental trip.”
The weatherman who ends up as the captain of the iceberg trawler Tonopah Maru is Paul Carpenter. His lover Jeanne gets him the job:
“Of course, for Samurai. A change of career track is something I can’t manage for you. But I can get you a transfer, if you want it. Iceberg trawler called the Tonopah Maru, getting ready to sail out of San Francisco, commanding officer needed, Salaryman Level Eleven. Came across the Personnel node this morning. You’re Level Eleven, aren’t you, Paul?”
Carpenter didn’t want to seem ungrateful. She was a dear woman and had his interests at heart. But he was baffled by all this.
“What the hell do I know about being commanding officer of an iceberg trawler, Jeanne?”
“What the hell did you know about being a weatherman, or a chip-runner, or all the other things you’ve done, until you did them?”