I think that naming the rarest regulator is difficult, but I will present some rare Scandinavian regulators.
B.t.w. talking about the CG45 as rare needs to be defined, maybe Eric can tell if it is the big label or the military CG45 that is the rarest

The square Cousteau Gagnan regulator is so sweet, thank you for sharing Eric
A friend of mine got a copy of the drawings for the square Cousteau Gagnan regulator in the beginning of the fifties (and I got a good lead in finding the drawings , stay tuned

). Afterwards he manufactured two dive able replicas, but booth was stolen some years ago

The father of my friend was a U.S. naval officer during WWII, and on one of the fathers post war journeys to the U.S. he got this rare CG45 / Nemrod to replace my friends home made regulator

1952 Ingmar Elfström pre Aqua Sport Prototype
One made
One known

1954 – 57 Swedish Diving Club: “Poseidon” (Pre Aqua Sport) Senior
Numbers made: 25
Two known

1958 Aqua Sport Senior
Numbers made?
Two known

1958 Aqua Sport Junior
Numbers made?
Four known

1956 Danish single stage balanced HGO prototype
One made
One known

1957 Danish single stage balanced HGO
Numbers made: 18
One known

1959 Danish Sea Horse
Numbers made: 10
Three known

1960 Danish Villy Arp
Model I
Numbers made?
Four known

Model III
A Series
Numbers made?
Two known

B Series
Numbers made?
No known examples
C Series
Numbers made?
Two known
Best regards
Niels
"Life could be worse . . . I could be Sting" Ozzy Osbourne