Sanspo posted an interesting article about the remaining traces of the Showa era in baseball disappearing. I'll list out some of things mentioned in the article down below:
Noriyoshi Omichi (41 y.o.) was selected by the Nankai Hawks in 1988. He was with the team when they were sold to Daiei and moved to Fukuoka from Osaka and became the Fukuoka Daiei Hawks in 1989. And again when the team was sold to Softbank after the 2004 season and became the Fukuoka Softbank Hawks. He was the last active player that had a connection to the Nankai Hawks team. Now that Omichi is retired, he plans on heading to the US next year to get some training as a coach with the NY Yankees.
Koichi Hori (41 y.o.) was selected by Lotte Orions in 1988 and spent his entire career with the team. So he was with the team when they moved from Kawasaki to Chiba and became the Chiba Lotte Marines in 1992. Hori was the last active player that had a connection to the Lotte Orions team.
There are currently 5 other players that have played for teams that were established during the Showa era (1926 - 1989) but no longer exist (and excluding the Kintetsu Buffaloes since they merged with Orix): Satoshi Nakajima (41 y.o.) started his career with the Hankyu Braves when he was drafted in 1986 (became the Orix Braves in 1989, then the Orix Blue Wave in 1991, the Orix Buffaloes in 2005); and four players that started their careers with the Taiyo Whales (became the Yokohama Bay Stars in 1993) -- Daisuke Miura (36 y.o.) when he was drafted in 1991; Motonobu Tainishige (39 y.o.) when he was drafted in 1988; Takuro Ishii (40 y.o.) when he joined the club in 1988; and Takashi Saito (40 y.o.) when he was drafted in 1991.
If you include the Kintetsu Buffaloes, then there are players like Norihiro Nakamura (37 y.o.) and Naoyuki Omura (34 y.o.).
There also aren't very many players that started their careers during the Show era. In addition to Nakajima, Tanishige, and Ishii, there are players like Kimiyasu Kudo (47 y.o. and drafted in 1981), Masahiro Yamamoto (45 y.o. and drafted in 1983), and Takeshi Yamasaki (42 y.o. and drafted in 1986).