Yes it can be done by you. time depends on configuration of the gunwhale that it runs along for your access. When you pull your old out attach a line to it so you can pull the new one back thru.

Do what Onemorecast said and if it doesn't fair better, start looking for a part number on the plastic jacketing, which will make it easy to order a replacemnt.

If you replace might consider replacing the helm also.
There are several types of steering helm designs from teleflex. Go to their website and they'll tell you whats standard for the type/speed of boat you have and tell you how to measure for your new cable. Make sure you don't exceed the minimum bend radius during install, keep the unit lubed every one/two years and it'll go for another 25 years.