These four non-transistor pocket radios pre-date the first commercial transistor radio, the Regency TR-1. The 1946 Pa-Kette pocket crystal radio is the only set here that didn't use subminiature tubes in its circuit.
Other pocket-size radios pre-dating the Regency TR-1 include the 1948 subminiature tube radio Pocket-Mite, the c.1950 subminiature tube radio Tiny Tooner (Thanks to Eric Wrobbel for this info about the "Tiny Tooner"), and the classic 1951 Italian Allocchio Bacchini "Junior 1" 4-mini-tube radio.
At least two other radios incorporating subminiature tubes were released in 1954, possibly pre-dating the Regency TR-1: the 4-tube (all subminiature tubes) Grundig Mini-Boy, and the Silvertone 4212 (two subminiature tubes, two mini tubes).
The Koyo Parrot KR-4S1 (four subminiature tubes) also may have come out in 1954, but as far as I know its release date is still uncertain.