Kyran, I have been shooting these for over 20 years, but if your (future father?) is going to use real lead shot, then I would advise having the barrel checked over first. Generally Tanegashima were built real sturdy, but a look down the bore should tell you if previous owners cleaned the thing properly in past ages. Many are hideously pitted internally! If it's in good condition, and you follow a ritual of cleaning before and after firing, there should be no problems. Naturally if you want to be 100% safe, then not firing it at all, or firing with blanks to start with could be the sensible way to go.
If the *square-headed 'bisen' plug screw is a little loose, then a good trick is to wind some thin cloth (or kitchen towel) around the screw before inserting, in order to get a tight fit and prevent internal blow-back. It took me a while to figure out a good system for two of my regular guns which are also a little loose. Each time I check later to see how far the burnt powder has worked its way back along the packed threads, usually less than 50% of the way.
(*Tazuke-Ryu guns on the other hand tend to have a round-headed breech screw, meaning they do not have to line up with the edges of the socket in the butt, and will always therefore slot in.)
PS I have an almost identical example of a Choshu gun as yours, so if you need a reference as to the pan lid/cover, or ramrod, for example, I'd be happy to post a pic or two. Sawada Taira has a couple of pages of illustrated explanation about Choshu guns, but the book 日本の古銃 Nihon no Furuju is in Japanese.