I am a bit prone to getting that awful hitch in my voice at times. But for me it's not usually the song itself, but some association I make with it. Over the years I've learned that I can, with time, get the song back.
Presently I have "Parting Glass" and "Swing Low, Sweet Chariot" on my no-sing list, having sung them for a dying friend. I consider the temporary loss of a song a small price to pay for having shared those moments with him and his wife.
Now, Mrs. Highlandman, while not a cold person at all, has the most amazing control of her voice and can infallibly sing through tears. In my case it's the voice that cuts out first.
-Glenn