the action (distance from fret to string) at the seventh fret is just one place on the string. It is determined by the height of the nut (what the string rests on near the tuners) and the saddle (what the string rests on near your strumming hand). For example, I have a twelve string guitar where the height of the nut is actually lower than the first fret. This makes the action at the first fret very low, even though the action at the 12th fret (equivalent to the seven fret on a dulcimer) is about the height of a nickel.
Many dulcimers use what is called a -0- fret instead of a nut. Doing so will lower the action at the first fret to less than that of a dime. The action at the seven fret is determined by the height of the saddle for these instruments.
The ease of pressing the strings depends on the string action along the entire length of the fret board. Most players spend 80% of their time below the seventh fret. If you are truly looking for an instrument with easy action, look at the nut height and action at the first fret.