OK, the tube only needs enough grease in it to prevent rusting and seizing up.
Many many motors don't have a zerk on there.
You just undo the steering cable every few years, apply a bit of grease to the steering rod, and put it back together.
Most of the steering rod actually will protrude out the port side of the steering tube, and can be greased without disconnecting it.
The only exception would be if the boat is used in saltwater.
So, you don't need the zerk. and the grease will not all leak out if you use a waterproof marine grease.
But, the broken sheath on the steering cable is another situation.
You did not break the sheath when you greased the zero, as there is an oring seal between the zerk and the cable.
But the broken sheath on the cable is a safety issue.
Your cable could bind up.
Or, it will rust internally, and then fray, break, or bind up.
You do not want this to happen while underway or you will go for a wild ride.
Be safe, replace the steering cable with one of the same length.
Oh, BTW, you do not (can't) grease the cable inside the sheath.
It is greased and sealed, and will be fine for many years, until the outer sheath dies of old age.
When you do replace the cable, remove the old cable and clean out the tube on the motor, using a
wire brush, like one used for cleaning the bore of a shotgun.
Grease the new steering rod and insert into the tube. Secure it and connect the port side, and you are done.