Capo positions, tunings, chords and other wonderful things
General mountain dulcimer or music discussions
No need to retune. A 'D' chord in DAD sounds the same as a 'D' chord in any other tuning, the fingering changes when you retune.
Look at it this way, a capo changes the order of the notes available in a tuning. It does not change the notes available in that tuning. Retuning changes the notes available on the instrument. You can prove this to yourself by checking the notes on each string with/without a capo and retuning and do the same thing.
Tuning and note order [capoing] are not particularly relevant to playing chords. They may change the fingering. As long as you have the notes available for a chord, and they are reachable, you can play that chord. Chording is very focused, it is playing 2-3 [or more] notes at a specific point in the tune.
For your own information try writing down the chords you need for each of the songs you will be playing. Then do the same for the chords you can play in the DAD tuning. If all the songs are in D or G, then you need to know the chords D, G, A, C. The notes needed for those are D, F#, A, G, B, C#, E, and C. Note that I only specified notes, not tuning. Find those on your dulcimer, they are all available in DAD. It is acceptable to use only 2 of the three notes of a chord, the first one and the last one [called power chords].
When the capo is used to change the tuning/key it is changing the first, lowest, or root, note of a scale. It is not changing the notes available on the dulcimer.
Just a note, if you have 1+ on your dulcimer, you can play the chords [C, F, G] in key of C. The 1+ adds the C and F in DAD