My first thought would be Nervous Norvus whose most famous song was Transfusion which we owned on a 78 rpm record when I was a child. I think from memory that the B side was called Dig. I'm having trouble finding a song list for him so I really don't know if he did a parody of Mr Sandman.

Coincidentally, yesterday I just watched the movie Weird: The Al Yankovic Story, and Nervous Norvus was mentioned once.