As you may know, there was a trend in the 1950s and 60s for TV stars in the US to record a cash-in single or album. Some made many albums. There are too many to list, but few, if any, would meet your criterion of singing well.
Indeed, DJ can sing. I absolutely love that song. The Nostalgia Critic said he was an awful singer, sometimes he's a moron. I think Dwayne sang in another one of his movies.
That last post reminds me of Mamma Mia. Except in this case it was actually heard on film. Never saw it on stage and reluctantly went to see it not just the once dragged along by all the females in the family to the local cinema, but also again on holiday on Skiathos since I'd never been to an outdoor cinema (as opposed to a drive in which is another story - I'm in the UK), and it was actually partly filmed there, even though most of it was on the nearby Skopelos.
But having never seen a single Pierce Brosnan Bond film, I was mightily impressed that the actor could send himself up SO well by doing the 'dad singing at a wedding' thing. And so I imagine he's on whatever soundtrack was released.