Perry Mason started in 1957, and from what I've seen from the first season DVD, there are a few soft plastic phones in the show, but not many. Della has a soft plastic keyset on her desk and Perry has what looks to be a dark beige 500 in his apartment, but this is in black and white, so there's no telling colors for sure. But it did have the light numbers on the dial, as I recall. Mostly it's black 302s, black 500s and a variety of old payphones with the transmitter mounted to the base like in your pictures. It's amazing to me that they used such old phones sometimes and new ones other times.
I think "Perry Mason Phone" and "Lucy Phone" could be catch-all names for the same thing. While most people remember the 302 Lucy had, from 1956 on she had a black 500 set in the apartment and in Connecticut until 1959. And in Hollywood in 1955 they had a 202.
I'm waiting for someone on eBay to refer to a soft plastic 500 as a Leave it to Beaver phone. Only one person has said that to me so far, a childhood friend of mine, who took one look at my white 1958 soft plastic set with the fat cord and aced it. He said "That looks like it just came out of Beaver's living room."
Jonathan