I was offered, next to my current job, to hold a one-time workshop that is not within my work permit. The organisation offered me a generous travel expense (not salary, but way more than my actual costs) that should make up for the effort.
Could that be considered a side job? The school apparently has not much experience with foreign teaching affairs. Will anybody care?
The legal definition of wage (Labor Standards Act Art. 2) includes anything that functions as a wage, regardless of the name, e.g. salary, bonus, allowance etc., with some exceptions. I would say this is not one of those exceptions. (You can always ask a lawyer or the government.)
As for volunteer work (which this doesn’t sound like), see the following thread:
Btw, if your employer is a buxiban, and this workshop is not going to occur at an educational institution (buxiban, kindergarten, public school, private school etc.), you should be covered if you remain under the control and supervision of the buxiban (i.e. it’s still your employer, and this is just another class).