If the cable is otherwise intact and there are no breaks that you know of, you might try and lube it first. I get similar issues on some of our motorcycles. Check this out:
Or, some guy named Steve has written up a lubing procedure and published on a boating site...can't recall the name of it:
Here's a way to do it:
Disconnect the cable from the jet nozzle, it has a spring-loaded clip. Loosen
the locknut and remove the cable end and locknut. COUNT THE NUMBER OF
TURNS for the cable end, so you can put it back on correctly. Write it down.
There is a rubber seal that slides onto the metal part of the cable, slide it
off. Find a piece of vinyl hose that fits snugly over the cable housing (the
outer part). Slip this on and secure it with a tie-wrap. Fill the vinyl hose
with oil and pressurize it gently. (This is why I haven't written it up yet. You
can use a long hose and hang it from the ceiling and let the oil soak in for a
day or two. You can rig up a way to attach a bicycle pump or air
compressor. It takes very little pressure--too much will blow the hose off).
Try moving the steering wheel gently. This will help work the oil into the
cable. Don't force it! The other cable may be the one that has the problem
and you could damage it. Remove the vinyl hose, pack some waterproof
grease around the end of the cable housing, then replace the rubber seal.
Re-install the locknut & cable end, then attach it to the jet nozzle.
I used Mobil 1 because it's a low viscosity oil and will protect well. Any light
oil will work.
I'd recommend doing this every year for a boat that's used in salt water,
every other year for fresh water boats.
