Only instruments I've taken are a harmonica and a wooden, Native American type flute. Easy to carry, don't weigh too much, I think the flute comes in at about 12oz.
Don't own one of those mini guitars but a dry bag might work.
I'd be super careful about strapping it on the outside a pack though. I've been know to break a fishing rod by setting down my pack at the end of a long day, without giving a thought to what's strapped on to it!