Harder or easier to sing with are relative terms. It depends on your voice.
Any Mode can be tuned to any key. DAA is Ionian Mode in the key of D. Drop everything one note and you have CGG, Ionian Mode in the key of C. DAd is Mixolydian Mode, key of D. Again drop everything one note and you have CGc, Mixolydian Mode in the key of C. The strings that came on your dulcimer will easily tune down to C.
The only drawback to tuning outside of the key of D is that you won't be able to play together with most other dulcimer players (as they believe D is the only key!). But if you are primarily a soloist and a singer then there're no real problem.
In all Ionian Modal tunings, the scale starts at the 3rd fret. All Mixolydian Modal tunings have the scale beginning on the open, unfretted string.
Modes are scales, like do, re, mi, fa, sol la, ti do -- which just happens to be the Ionian Mode scale. The Mixolydian Mode scale is do, re, mi, fa, sol, la, ti-flat, do. Any Mode (scale) can be in any key. Generally the keynote of the dulcimer is the note to which the bass string is tuned - A, B, C, D, E, F, G
To understand the interrelationships between Tunings, Modes, Scales, etc, I recommend you read my blog article here called Uncontrite Modal Folker : http://mountaindulcimer.ning.com/profiles/blogs/uncontrite-modal-fo...
My other article, called I Just Got A Dulcimer, Now What? Answers many beginner questions about tuning and playing, care and feeding, and an illustrated glossary of terms of the dulcimer. It's here:
http://mountaindulcimer.ning.com/profiles/blogs/i-just-got-a-dulcimer-now-what