From what I'm understanding on this board, portables would have been around, but not readily available to just anyone. Most likely, only those who could afford them. This would have been a transitional time when the price was just beginning to drop. You could probably equate this to someone having cable TV in the late 70's, a CD player in 1981, or a home computer in the very early 80's. They were around, but not a staple in every home, and if someone did have these things--well, they were a real hot shot, as my granddaddy used to say. Someone all the neighborhood kids would probably be envious of.
So in considering your story, I guess the real issue would be if your character who is going to be using the portable radio would be that type of someone, or would know someone like that. If you can make that a credible issue, most readers, I'm sure, would buy it.
Also, it might pay to consider the geographic region of your story. I've lived in the South and been a Southerner all my life, and it's no insult, only honest fact, that we generally tend to be a couple of paces behind the times, at least when it comes to new innovations, fashion trends, etc.
So even if a lot of people may have been carrying portables on the West or East coast, the trend may not have trickled Southward, or been very widespread, until 2-3 years later. I don't know where your story is set, but that's something to consider as well.