You're right about that, Brian.
The first line is indeed missing from James Ironhead Baker's recording.
I was confused when I listened to it again because many other versions begin with "Early one morning, one morning in may", but that is actually Ironhead's second line.

I'm adding a selection of recordings of this song family, including Ironhead Baker's to soundcloud at the moment.
I'll post them when I'm done.

It doesn't help much, but I noticed that John A. Lomax made two recordings of Ironhead's version, of which only one was released comercially.

First recording, sung by Ironhead Baker:
The St. James hospital - James Baker (Iron Head)
This is probably the recording that we have.

Second recording, spoken by Ironhead Baker:
St. James hospital - James (Iron Head) Baker
It is possible that the first line is included in the spoken version, but we have no way of confirming this without access to the recording.