I've seen a lot of zip ties in other newer appliance electrical systems. I did not think of the ties but they will work. They won't rust, won't chemically interact with the wires so I see a good idea there.
I have no source for the OEM clips. The ones I have used came from the motor they were on. The extras came from a busted motor I took apart. You do have to be careful when you unlatch them. Other than the 90º angle on the one end there is nothing holding the pieces together.
Joe