Yes. Japanese Army officers of the time were issued the shin guntō, meaning "new military sword." For example, this site has pictures and information on the shin guntō pattern that began issue in 1938. IJA NCOs had their own, less elaborate shin guntō as well. These swords were often made with modern construction techniques, but in form and size they are clearly based on the katana. Whenever people talk about "samurai swords" being used by Japanese in the Asia-Pacific, these are the "samurai swords" being referred to. Guntō were issued en masse, and many became souvenirs for Allied troops at the end of the war, and as such are fairly plentiful in the antiques market even today.

As for martial arts, well, I can't comment on how many IJA officers would have been proficient in the subject, but martial arts does have a long tradition in Japan and it is not out of the realm at all to think that this officer might have trained in some form of martial arts prior to joining the Army. Lots of "popular" schools of martial arts cropped up in the Meiji era (the so-called gendai budō).

I can see why having an IJA officer who is proficient in martial arts and equipped with a sword in 1942 in a work of fiction might seem very cliche - it's like a combination of Japanese stereotypes. However, on must remember that the Japanese leaders of the time was focused on creating a national image of Japan by blending elements of its long history - particularly the idea of the samurai and bushidō - with very modern, nationalistic imagery. By issuing the shin guntō, the IJA was deliberately trying to create some sort of connection with the samurai of Japan's feudal era. It's a bit like how Mussolini wanted to portray his Italy as a new version of the Roman Empire, except the Japanese were far more succesful with their propaganda than Mussolini ever was. Japanese propaganda was so succesful that the 20th century, nationalist "bushidō" is commonly and incorrectly assumed to be a trait of Japanese society that has existed throughout its history.

If you have access to JSTOR, this article talks a bit about how modern bushidō basically an invented concept. It was certainly a very useful ideology - without it, it's unlikely that the Japanese would have been able to get so many pilots who were willing to ram their aircraft into enemy ships, for example. The fact that it is seen as such an essential part of Japanese military history and culture to a level of it becoming a "stereotype" shows how effective Meiji through Shōwa period propaganda was at shaping our view of Japanese culture.

During that time in Japan, the sport of Judo was heavily propagated as a quintessential and unique Japanese art. It was a required subject for boys in school from 1931. You could expect most soldiers to have familiarity with it, at least. Its promotion at that time was closely entwined with the Japanese fascist ideology of the time. So while it might be a racist stereotype to portray a martial-arts-using soldier, at the same time, there was an historically specific precedent. Baseball was still more popular in Japan at that time, though. And it wasn't any martial arts that had this significance--it was just Judo.

Very plausible and not at all a racist stereotype.

As has already been pointed out, Japanese officers were issued swords. My father owns one, which was purchased by his father shortly after the war ended.

Martial arts such as judo and kendo were very popular in the Japanese military. For example, this page shows some nice photos of IJN officers and their dojos.

Even in today's Japanese SDF, hand to hand martial arts (kakuto jutsu) is part of training. And I have met a few SDF guys who practice judo and kendo in their spare time (just as many military men around the world practice various hand to hand martial arts).