I checked JC's ABC Tune finder and the only version of Iron Legs Hornpipe that came up was the one Jack Posted.

The alternative fingering for D' on the Dolmetsch website is in fact slightly flat which probably explains why you find the two D's different. I agree with Jack that this alternative is not actually a lot of use.

What you can try is alternative fingerings for E'. There are three fingerings for E' on a C recorder (A' on an F recorder) all of which are in tune.

The usual one is
x 123 45--
You can also try
- 123 45--
or
- -23 45--

Try each of these in turn and you should find no noticeable difference in the note.

A further thought;

Try leaving fingers 4 & 5 on while fingering D, thus;
- -2- 45--
Adding 4 & 5 has almost no effect on the D and means the "dede" can be played by moving just one finger, LH finger 3.

Similarly leaving 4 & 5 on for C' works for the "cece" sequence. There is a slight difference compared with the standard C' fingering, but it is unlikely it would be noticed in a quick passage.