Rachel, I'm not quite sure what you mean by "interchangeable," but a chord is a chord regardless of the instrument.TheC major chord, for example,is comprised of the notes C, E, and G. If you play those notes at the same time you are playing a C chord. It doesn't matter what instrument you are playing. Similarly, G major involves the notes G, B, and D. D involves the notes D, F# and A.
Remember that the chords only provide the harmonic structure of the tune and do not sound like the melody. If all you do is play the chords, it may be hard to hear what song you are playing. Only a few--like "The 59th StreetBridge Song (Feeling Groovy)"--will be easily identifiable.
Why not start with a simple, two-chord song? Play "Go Tell Aunt Rhody" with the chords D (002) and A (101). Strum the chords while you sing (or whistle, or hum, or whatever). For the first line, strum your D chord. For second line, strum the A chord. For the third line go back to the D chord. And for the fourth lineplay the A chord until the end when you resolve to the D again. The first line of the melody is the note you make when you play the melody string on the second fret. Try playing those chords and singing. Do the chords seem to accompany the melody correctly?
Stephen Seifert's chord chart is an excellent chord chart, but you might not be ready to use it on its own if you are just beginning to play chords. Instead you need to gain practice fretting and strumming chords and understanding the role of chords in music. Once you learn that, then you can use Stephen's chart as a resource to learn how to play chords all over the fretboard and how to play some more complicated chords.
One way of playing the dulcimer is indeed to strum chords as backup to the melody or lead being sung or played by another instrument. But many of us who play chords do so in what is called a chord/melody style in which we combine chording with playing the melody. In that style of play, the melody is more easily identifiable than it is if you just strum chords as backup. Another style--in fact the traditional style--of dulcimer is a drone style in which the melody is played (either with fingers or a noter) on the melody string and the other two strings are allowed to ring out (drone). In that style of play as well, the melody is easily identified.
But if you are just strumming chords, you will likely not hear the melody from your strumming alone. That is why I suggest you hum or sing or whistle the melody and play the chords as backup.
updated by @dusty: 02/12/16 04:58:24AM