I pulled out the Deso and Canyonlands Belknap Guides and checked this out.
If you put in at Cisco (the Westwater takeout) you can float the Colorado all the way to Potash which is 60 miles or so. The last day or so down to Moab has several Class II rapids and maybe one Class III that are easily navigated.
On the Green, you can put in at Green River and float Labyrinth Canyon to Mineral Bottom. The float from GR to MB is about 68 miles and has one Class I riffle. The drive down to MB is Class IV for anyone with a fear of heights. Putting in at Swasey's would add about 12 miles and one rapid (Tusher) which I don't know anything about except that if I haven't heard of it its probably no more than Class II. You can also put in at Ruby Ranch to take 23 miles of low rolling country off the Labyrinth Canyon stretch.
Have a good trip!
Nothing in the world is more yielding and gentle than water. Yet it has no equal for conquering the resistant and tough. The flexible can overcome the unbending; the soft can overcome the hard. - Lao Tse