Versions of Bobby Shaftoe I can find seem to mostly be in G with a range of an octave D to d.

It sounds like the "wooden recorder" you got was a tenor (recorders of any size can be made out of either wood or plastic). It should have a range of *two* octaves and a tone from middle C without trying too hard, so the tune should fit. But unless the recorder has an unusually strong lower register it would be more effective transposed to D, which would give it a range from A to a.

Perhaps you could post an ABC of the exact version of the tune you've got, or a link to a scan or sound file of it.