It may be possible to use the original wire as a messenger to pull the new through - though creating a compact temporary splice can be a challenge. Also any fittings/cable ends can complicate this procedure.
1984 Fast/Nicholson 345 "FastForward"
".. there is much you could do at sea with common sense.. and very little you could do without it.."
Capt G E Ericson (from "The Cruel Sea" by Nicholas Monsarrat)