I have just (almost completed) my strum stick cane dulcimer and was left wondering which way to string it. I set it up with DAD tuning with the high D or small string at the top. I figure once it is given away, my 91 year old Dad can decide if he wants to play it in his lap or like a guitar. I'll swap the high and low strings if he wants to play it like a guitar.
It is playable at the moment but lacks the last coat(s) of tung oil finish and the cane tip. Otherwise, I'm really happy with the build.
Anyway, I just crossed this bridge myself... trying to decide which way to string it and do believe you will want the high string at the belly if you play it laying on your lap.