I think it might be asking too much of the professionals to be stuck with an outsider for a day. The apprentices could easily get in the way or prevent the pros from doing everything they need to do.
Perhaps this idea could be approached differently though, maybe you can get someone with expertise in the desired field to give a tour of a "typical working day".
A young med student, for instance, could earn some extra money by taking the apprentice through their normal schedule and showing them around allocated areas of the hospital. Or a law student can sit in a court session with the apprentice and explain everything afterwards.
I think, in this way, apprentices still get the information they are after, whether it be for interest or to help them decide on a career path. Students or retirees get an opportunity to make some money. And the professionals don't get irritated by having to take care of another obligation piled onto their already full working schedule.
Like I said, if the professionals are willing, then the idea is perfect as is, I'm just wondering if they will be able to remain patient and give enough attention to the apprentice if they are busy with their actual work. I think emergencies might arise, which could force the pro to ditch the apprentice, or even just become stressed and lash out at the apprentice/customer for being in the way. By getting someone knowledgeable who is dedicated to only the customer these risks are eliminated.