Should I clean and regrease the CV joints?

affirmitive.

 

An excellent idea to change the transaxle ATF periodically. I would leave the CV joints alone if the rubber protective boots are in good condition.

 

I think this is a good idea along with new rubber boots.

I had a front wheel drive car that I used to tow a caravan with (not a Prius, but identical system) on a regular run.

The CV joints made no noise and everything seemed fine, but on one stretch of road after climbing a long hill I got a violent steering shake. After slowing down after a short distance this shake stopped. This happened repeatedly on this section of road.

After many hours of trying to trace the problem I found in one of the CV joints the grease had dried out ( no split in the boot) cleaning and re greasing cured the problem.

 

I think its an excellent idea too. Whats your plan just cutting the band off and pulling the boots back?
Flushing them out and regreasing them?
Here's the worlds best chassis/cv joint grease. This stuff is like candy 100% pure synthetic base stock olefin:

Red Line Synthetic Oil - Grease and Assembly Lube - CV-2 Grease

While your under there spray grease the entire suspension front & back too. I use this stuff its the best product ever. No smell and it stays where you spray it. Get the control arm pivot bushing area and anything thats starting to corrode. I use it on all my cars and no sqeeking or clunking and not a bit of rust on the undercarriage. Get all the door hinges and the hood latch and hood hinges. Found at Home Depot:

Blaster Corrosion Stop Protectant - PB Blaster

And when done spray the boots real good with this stuff. And get the rubber bellows between the door jams that protect all the wiring. Works real good and smells nice:

Pro-Shine Protectant | Black Magic Car Care Products

 

There's a little bug in the new software here. If you post a link and then you open the page back up to edit the page it leaves the link wording but kills the link itself. It killed my Redline CV Grease link.

 

post the pics of the DIY setup