I found a place in Denver that rents them but all they had was a 25hp or 50hp motor that would not only be overkill for a raft but also way heavy. I started a thread last year about this too, and ended up just buying a used 5hp 4stroke off one of the members here. It needs some work, so I'm not prepared to rent or loan it out....sorry.
The other complication with renting one is that a Marina or classic hardshell boat service isn't going to have a way to mount said motor to a raft.
My understanding of getting your boat licensed is that the boat itself is licensed not the motor. You do this by going to a Parks and Wildlife office and getting one. You will then have to either paint the registration letters on your boat or make a plaque with them and hang it off your frame (the prefered way IMHO). Rafts can be a bit hard since they don't have serial numbers that are recognizable by the Parks and Wildlife people so they may have to give you a new number or something.
The only stretch I've used a motor on was Desolation, and they couldn't give a crap. I didn't know about the registration the first time and they "looked the other way" and I was a dumbass and forgot my paperwork the second time and they did it again.
Since Cataract spits out onto Lake Powell, it may be a bigger deal if you get caught without the registration. Just so you know, there is current all the way to Hite the last I checked, so a motor isn't strictly needed for after the rapids. It will probably make for faster travel on the flatwater above the confluence and will certainly expedite getting out of the canyon if that is what you want, but it isn't strictly needed to run Cataract anymore.