Canyons are inherently risky. Flash floods occur without notice on sunny days. Technical skills & surrounding topography knowledge required yet does not eliminate risk.
Rattlesnake Canyon is the lower tributary to Woods Canyon. The trail data given reflects a hike from the rim to Woods Canyon and back. The canyon is named after the rigid ride to the rim which rattles your nerves. Okay, I made that up! One thing for sure, you won't forget the ride.
The road actually goes down a couple switchbacks before you must park. It's steep but the tilt inward would likely put your nerves on end. There is plenty of room to turn around at the end if you dare. I highly recommend parking at the first sight of the canyon.
Where the road ends you'll have to search a bit for the trail going down. Best described as at the end to the left. This really isn't a maintained hiking trail so it's likely to be overgrown. The route is for workers to service the water gauging station. The trail quickly works down to the bottom of the canyon. An early morning start puts you in the shade. The trail takes you right down to the gauging station. Another twenty feet or so and you come to a steep waterfall. There wasn't much water flow on this trip. It appears to be an awesome site when the creek is flowing.
Now comes the big obstacle. A thirty foot waterfall with canyon walls on both sides. One thing for sure, it's steep! I looked at it and decided to pass. However, I do believe it can be negotiated. It appears to be easier getting up than going down. Should you be nuts enough to give it a go, read that little disclaimer at the bottom of this page. Since I didn't complete the hike I can't say for sure what you'll encounter. The canyon appears to be a small boulder scramble most of the way to Woods Canyon. If my estimates are correct you should come out just south of "Red Rock Beach" in Woods Canyon.
If your a wimp like myself just check out the canyon going away from the waterfall. There's nothing spectacular to mention. The trek is a constant boulder scramble. If you're just passing by to Flagstaff, the hike down to the waterfall is less than an hour roundtrip.
WARNING! Hiking and outdoor related sports can be dangerous. Be responsible and prepare for the trip. Study the area you are entering and plan accordingly. Dress for the current and unexpected weather changes. Take plenty of water. Never go alone. Make an itinerary with your plan(s), route(s), destination(s) and expected return time. Give your itinerary to trusted family and/or friends.