The Buddy has an "always on" pilot flame. I'm not sure about the Wave, I don't think so. Maybe Kerry would be able to tell you.
I have used the Buddy but I place it on top of my stove lid not on the floor where a blanket or dog could accidently go " puff " !
My camper is a small non slide so I only use Buddy when I travel alone, only during the times when I'm awake . Heavy sleeping bag at night works.
IMO, having two persons on board and a large dog is not the best idea with the open flame, I just use the OEM furnace then.
If I had a Wave maybe I would feel more safe, I don't know .
Im not sure but I think the vented cat uses some 12 v power , the PLAT Cat . But that's a VG safe heater.
Bob