I think it is a big mistake to concentrate on 'safety' or mix of science/math when choosing a career. What you need to consider is what those in the field actually do and whether you can put yourselves in those shoes. In terms of scientific fields, the papers that are written
. In terms of engineering, the procedures that are followed to complete a project. Medicine has a huge range of possible niches in that regard, but you still have to waste a lot of time 'paying your dues' practising on the frontline until you can work towards those niches.
And so it goes for all the other possible careers
Next, once you have narrowed down the list, you will need to ask people in those careers lots of questions. From the proportions of time spent on each aspect of their jobs, what frustrates them most about their job, to future career prospects. The only way you will really know what you are getting yourself into is by talking to real people in those fields. And that means that you will need to contact people who aren't on forums like this one. Don't get caught up on career questionnaires or career advisors either, nothing substitutes for talking to real people and putting yourself in their shoes.
If you have a month to decide, then you should be spending much of that time solving this question, rather than deciding prematurely.