I have a person in mind who works for another company that I would like to apply for a job with my current employer. This person would be a perfect fit for several reasons, but they are in another country and the only way I have to get in contact with them is by using their current work email address.
If I contact them via this person's current work email, am I setting them up to get in trouble if their boss or some other employee sees the email? I do not want to get this person in trouble and I'm not sure how to proceed.
Mentioning that you want them to apply over their existing work e-mail is a spectacularly bad idea.
Their bosses could easily see it and you could get them in trouble/fired.
If their bosses don't see it the above possibility may well occur to the recipient and they may form an opinion of you/your approach that is less than favorable ("how could this guy put my employment at risk", "is this a trap?" etc)
Your best bet is to find an alternate way of contacting them (LinkedIn is a decent one in this scenario as it remains firmly within the "professional" world).