I certainly am no chemistry/tox expert, but have a few thoughts. The routine urine tox panels are all specifically directed at the metabolites of drugs of abuse. In this type of test they will not find anything they are not looking for (barring cross-reactivity). Finasteride is a steroid, they would have no reason to look for that. If this were an athletic doping test it would be another matter.
More in-depth tox analyses (forensics stuff) involve mass spec and there, they will see everything and try to explain every peak. I guarantee that no one is doing this for a summer job pre-employment study. The hospital has bigger fish to fry than super sleuthing about your medical problems, they just want to make sure you are not a junkie.
Just take the test, don't fret about the finasteride issue, don't volunteer the information or do anything special and there is a 99% chance you will hear nothing about it. If it does get flagged, they will give you a chance to explain to the occupational health department (presumably an occupational health physician) and you will have a pretty good story and they will keep it quiet. I understand you don't want to discuss it, but the odds favor you and this may just be one of those things you have to do. If you are going to work in the medical field (or most other fields, or apply for health or life insurance), this is not the last time you will face this issue. Consider yourself lucky to not have something harder to explain, like an actual drug problem or a criminal record... unless you also have these things, in which case good luck...