That would perhaps be the best bet. What's remarkable is that I can't even recall such an early recording of a electric piano that sounds like a Fender Rhodes. Were they (Rhodes pianos) even manufactured by 1961?
Yes.
From wikipedia:
1946-1965: Harold Rhodes subsequently founded The Rhodes Piano Corporation and introduced the Pre-Piano at NAMM 1946.[6] In 1959, Rhodes entered a joint venture with Leo Fender to manufacture the instruments under a company named Fender & Rhodes. The partnership lasted for six years with the model marketed as the Fender Rhodes Piano Bass, a 32-note version with only the low range of the piano, accounting for the bulk of the sales. The Fender Rhodes Celeste was a similar keyboard covering the midrange of the piano, and electric pianos with tube amplifiers were prototyped at the time. The Piano 73 would become known as the Fender Rhodes Electric Piano, with an amplifier cabinet used as a base for supporting the piano keyboard.[5]
I agree thought that it's unusual to hear one on recodigns of this vintage. Usually I hear Wurlitzer sounds on those.