I am assuming this is a hurricane since you talk about the plasic sheathing.
You need to order the cables from Hurricane www.mauifiberglass.com, Or we have them in stock and ready to ship. www.oceanohana.com The basics of changing the lines out are as followed.

1. Cut old lines from rear of boat,
2. Tie them to the new lines.
3. Pull through to the front.
4. Loop the connectors together
5. Repeat steps 1-4 on opposite side.
6. When you re-attach the rudder to the plastic fitting be sure NOT to tighten the set screw too much, It only needs to be finger tight., Overtightening will crack the fitting.

It really is easy to do and takes about 5 minutes. The plastic sheath may be able to be replaced on it's own. I have not tried it but my idea is to undo the connectors at the front, Tie fishing line to the rudder lines, Pull out from the rar of canoe. Atatch a shrink wrap tube and shrink. Pull lines back throgh and re-connect.
One thing to know about the Hurricane rudder cables is they are a number of lines, Not Stainless steel cables like older hurricanes or other boats. The lines look just like dental floss and their are 8 lines per side. This stuff is very strong.

It is always good to change out the cables yearly whether it looks like it needs it or not. Take if from experience it is no fun being 2 miles offshore with no steering. You didn't say where you live, here in Hawaii or mainland?