This is a very cool question, and I'd love to have the chance to answer it.

Although in the 16th century there were many cases of Portuguese soldiers serving as mercenaries in various Asian realms, the most important examples being the Portuguese mercenary communities (and kingdoms!) in Burma - which was then going through a "warring-states period" of it's own - there actually isn't any recorded case of relevant Portuguese mercenaries in the service of any Japanese lord, beyond one or two very displaced "military specialists" if we can call them that. This is because the nature of official Portuguese policy regarding Japan was basically limited to dispatching one or two large ships from Goa to trade, which, stopping by Malacca and Macau before reaching Japan, represented an incredibly lenghty voyage (because of the stops and the monsoon patterns, it lasted well over a year before returning!), but also extremely profitable, meaning the ships were few and carried just enough soldiers to defend it's valuable cargo from pirates - a handfull. Thus, there were never many Portuguese soldiers in Japan to constitute a fighting force of their own.

For this reason, unlike in Burma, in Japan the Portuguese were really most significant in the "civil" part of society, either as simple merchants, such as a nucleus of neighbours settled in Nagasaki and married to local women, or as specialists, like Fr. Luís de Almeida, who in 1556 opened the first modern hospital in Japan, in the town of Funai.

Do note however, there is a distinction here between "mercenaries" (whom the Portuguese referred to as aventureiros) and soldiers in offical crown service. The only Portuguese ships allowed to sail to Japan were Crown property, and their captain represented the Crown.

So although there wasn't an important Portuguese mercenary presence in Japan, it is relevant to note that the Portuguese did officially participate in one or two military actions in Japan: In 1556, for instance, through the mediation of Portuguese Jesuits, the Japanese Christian lord Otomo Sorin obtained the assistance of three Portuguese ships then present in Japan, to siege the coastal town of Moji; it was successfully stormed after a naval bombardment, a very familiar operation to the Portuguese in the Orient.

Similarly, in 1565, two Portuguese ships anchored by the town of Fukuda repelled a Japanese fleet of junks and boats that had come to plunder them, but this was much more circumstantial.

Sources:

The Great Ship of Amacon and The Christian Century in Japan by Charles R. Boxer.

Portugal and Japan: The Namban Century by João Paulo Oliveira e Costa.