Working?  Do you need the pay?  Once they discover you’re “one of them,” rigid, divisive types who go to the Latin Mass, unless this diocese or parish is very unusual, they won’t hire you or accept you to volunteer.  If you conceal it and are found out, you’ll be fired or blacklisted.  There will come a point where you can’t do or agree to something.  The only exception may be if your job is janitorial, maintenance, groundskeeping, or security guard.

I think everyone here has already concluded that there's nothing inherently wrong with it.

I think the real answer is going to be in the ACTUAL school and your personal impressions of it. Some parts of the country(world) are more liberal than others. Some places are surprisingly receptive to real Catholicism as long as you don't get into specifics about the New Mass or V2. The ages of the children you're helping would also make quite a difference.

I taught First Communion at a NO church right as I was discovering Tradition. It's a small church and the textbooks weren't "latest and greatest", but there was nothing in those books that I wouldn't teach today. Other than the graphics being of the NO Mass, the topics were essentially the same as I teach my own children when preparing for First Communion. Plus, there was no oversight, so I could have been teaching them anything I pleased.

I think the most likely obstacle you're going to have is whether or not they expect you to attend / participate at Mass. Catholic schools here have the students attend weekday Mass once each week during the school day but I've heard that it's optional since they welcome students into the school who aren't Catholic.

Long story short, your own judgement is going to be the best answer in this situation. Just be honest and you can always leave if the school is worse than you expected.