This depends on the culture, the instructor, the hosting institution (a museum? The instructor's workshop?) and how much information the instructor reveals in the introduction.
I can answer for the US, but not for Japan or other countries.
Instructors usually expect to get paid to part with specialized skills, both the presentation and the practicum (practicing the skill.) If the class size is small, e.g. to allow for a lot of personal interaction, then I would not ask the instructor if you could sit in, especially as it is an expensive workshop. Asking puts the instructor in an awkward position.
If the class size is large, such that they break down into smaller groups for the practicum, I might ask to sit in, and if permitted to sit in, I would not take any handouts or ask any questions.
If the instructor is passionate about his art and wants to spread interest as much as possible, they might welcome you to sit in (the fact that the workshop is costly may indicate that such might not be the case.) You might be welcome in a workshop held in a museum; I would not ask if it was in the instructor's home/workshop.
I used to teach a workshop. It took me years of reading and experimentation to become skillful at what I taught, and I would not take too kindly to someone wanting to learn what I had to impart for free. Yet there were other things that I loved and taught for free.
how would I go about requesting this with the craftsman
Ask when you're purchasing your wife's attendance fee.
I've no interest in the skill myself, but I feel odd giving her a gift to do completely on her own. Ideally I'd like to go with her, and sit at the side, so that afterwards we can still talk about it, etc.
Maybe cultural, but there are lots of things married people do independently of each other. I had no interest in golf or squash/racketball. "How was your game?" was as much as I wanted to know.
You might actually have more to talk about if you don't go to the presentation. She can be the "expert" and you the "student". You would have questions to discuss.