You can try that, but I am guessing that the cable wears inside the sheath and gets stiff. First thing you have to do is verify that that's the fault. If you're doing this yourself, I hope you're not too big of a person and are pretty flexible because it is one of the worst jobs I have done on a boat.
That, or just bit the bullet and pay to get it done. Here's pix from my ordeal replacing the steering actuator. You can see I removed both exhaust manifolds to get at it, it was tough getting at the cotter pin under the steering arm to remove the cable end, but even tougher to remove the 2 big cotter pins that retain the bolts that hold the actuator onto the inner transom plate. My steering cable was still OK when I did this job (2021). I had to use a cotter pin extractor and various other tools to get those big cotter pins out. I lubed everything with Evinrude triple guard grease in case I ever have to do that hateful job again!