I've played n/d on 3, 4 and 5 string dulcimers and I've borrowed a 6-string once in a while. I haven't felt the need to adapt my strumming except for one thing: how the number of strings (and how they're tuned) affects the sound balance between melody vs drones.
If you're used to a typical 4-string setup (with a doubled melody course) then you're used to hearing 2 melody strings and 2 drones. If you try a typical 6-string with three doubled courses, you'll have 2 melody strings and 4 drones. Which might seem like too many drones. If the drones are (ahem) droning out the melody then you'll want to adjust your strum. Angle the pick so you're strumming the melody string(s) harder than the drones. Don't feel compelled to strum across all the strings at every strum, either.
If you're used to a 3-string, then maybe a 6-string won't be a big change. There are a lot of possible 6-string setups and tunings. I guess the only real answer is listen while you strum and adapt as you like.