Most of all my dogs and cats have dreamt. A few displayed actions like you described. A dog I had once would try to bite me if I tried to wake him anything more than very softly. It's like he (they) didn't know who it was but he was just startled and went immediately into defense mode protecting himself. Once he realized it was me he stopped his movement toward me immediately. The worst that happened one time early on was he nicked me with one of his teeth. I made sure from them on that I only put my hand on him near his back hips or butt but not his tail. Some dogs can be sensitive about their tails when startled. I would move my hand back and forth gently on his skin just to make him move a little bit. I've done that with the cats too and it seems to work. If you go about touching their face or their neck, they seem to have gotten more aggressive (in my situations) and I think that's because they're startled too much too fast and being too much literally in their face.
The more often you can catch them dreaming and wake them up soon, it's been my experience the sooner they get used to you doing that.
Although I don't remember ever trying this, I like the idea that @
Lilnonames mentioned about using food for them to smell to wake them up.
