This story (published 1988, per http://www.isfdb.org/cgi-bin/title.cgi?57386) is short (16 pages on my Nook), but has a lot of characters in it. I had to make a list to keep everyone straight.
Reis - male, second in command
Jan - female, lower officer
Hap - male, captain, severely injured or dead
Centcomp - the ship's central computer
Paule - female, lower officer, secretly married to Hap
Sid Dawson - male, lower officer or senior enlisted/NCO - maybe a medic
Nell Upson - female, lower officer, dead
Not that it was really confusing, but we get introduced to everyone in the first couple of pages.
Setting: on a far-solar ship (we find out that we are close to Neptune) that's been hit and severely damaged by something. It seems like an accident - asteroid strike, something like that. Several sections are damaged and it seems like maybe half the ship, "downship", is sufficiently damaged that the remaining crew think everyone there is dead. Reis is outside, cataloging damage to start repairs. He sees Upton's corpse and we get a gruesome description of what space will do to the body and that blood won't coagulate without oxygen.
Wolfe has some fun wordplay in here: Reis notes that the exterior of section 3 is "...peeled back like the black skin of a graphite-fiber banana...". Later, he is examining Hap (who's dying or already dead) and thinks, "Hap's face was greenish-yellow...it reminded Reis of an unripe banana....'So this is banana day', he thought." I laughed.
They put Hap's body in a medical pod, because he might not be dead, but they also need to get busy fixing the ship. Centcomp continues to attempt to resuscitate him, even though all life signs are zero. Reis (senior officer still vertical) tells Centcomp to stop and Centcomp goes all, "Sorry, Dave, I can't do that," on him. This is because Hap had given Centcomp orders to continue resuscitating any crew member as long at Centcomp believes there's a chance to bring them back. Which leads to an interesting question: what does a computer believe? What's the cutoff when Centcomp gives up: 1 in a million, 1 in a billion? Wolfe is, once again, challenging us to consider what and how a non-human intelligence thinks.
To better communicate with Centcomp, Reis puts on the "transducer headband" interface, rather than the keyboard/switches, stylus (aka rat-tail) tools he's been using. This is a direct brain-to-computer interface - very Matrix feeling in the description. Guess who's hanging out? Captain Hap! Or maybe Centcomp's avatar of Hap. This Hap wants to repair the ship and keep going on the mission (never actually clarified what this is) and, since he's still the captain, thinks any other course is mutiny (return of a theme from Silhouette).
I think Centcomp is taking orders from Hap and giving those to the other crew members. Maybe Hap was using the transducer headband when the ship was damaged, so his consciousness is actually there, or Centcomp is making up an avatar of Hap based on prior interactions/orders (like the resuscitation order). Reis loses a bunch of time while in the Matrix and is woken up when someone (something?) stabs him. This appears to be the ship stabbing Reis with one of the titanium rat-tails/styli on orders from Hap. Kind of a dick move, really.
Oh, and space zombies. All kinds of fun stuff happening in this story.