To my AmE ear, it sounds unnatural. Let's substitute the word "them" for "those dryers." "Which of them do you want?" works. "Which one of them do you want?" also works. But "Which out of them do you want?" doesn't sound quite right, at least to me. But if you can provide some support for using "out of" here, please post it and we'll have a look.
It seems it's usage and not grammar. "Out of" implies movement/position, but is also used figuratively with numbers. Nothing moves or takes position just by wanting it. Making it a number helps, but I'd recommend putting "which" last: "Out of those nine driers, which do you want?" "Out of all of those driers, which do you want?" You can reverse these of course. Once you've used "which" "out of" seems redundant unless separated by a comma. I think the direct "which" even clashes with the figurative "out of", just as you don't say "on last Tuesday", "in next month", or "three thirty o'clock" (though "on Tuesday of last week", "sometime next month"/"in the month after this", "half past three (o'clock)"). I hate to say just memorize it . . .