This version sounds the most like the one I recall from over 50 years ago...so glad I found this thread and relieved my troubled mind about these lyrics. About all I could remember were the "twilly willy willy witt bum bums" and the "sing toriay sing toriays". But I did remember that he never cured the ailment that the person had in my version...

Oh, I am Dr. Ironbeard, twilli willi witt boom, boom
I'll cure your ills with healing art, twilli willi witt boom, boom
Now I can make the dumb to walk, twilli willi witt boom, boom, boom, boom
The lame to see, the blind to talk, twilli willi witt boom, boom
Sing tor-i-ay, sing tor-i-ay, twilli willi witt boom, boom, boom, boom
Sing tor-i-ay, sing tor-i-ay, twilli willi witt boom, boom, boom.