I think nuclear chemists and nuclear physicists come at nuclear reactions somewhat differently. If I understand correctly, nuclear physicists to understand the mechanism and structure of the nucleus, and how they contribute to changes in the nucleus. Nuclear chemists are interested in how nuclear reactions contribute to changes in the atomic (i.e. electronic) structure. I am not sure the division is quite this stark. Why not ask nuclear physicists and/or chemists at you local (or any) university?
To work alongside a nuclear physicist/chemist you will probably do it during grad school at latest. You will not likely wait until finishing grad school.
I think nuclear physicists studying reactions are more likely to be in an academic setting. Nuclear chemists may be found in more diverse settings such as hospitals, the biological sciences, (irradiating foods may kill deleterious microorganisms), etc, but I do not know for sure. This may be a prejudice.
My guess, although I may have it wrong is, if you want to study with a nuclear chemist or physicist as soon as possible, chemistry is more likely to offer this chance, at the undergraduate level. For example, nuclear magnetic resonance is a common tool used in magnetic resonance imaging with ubiquitous medical application. However this medical imaging studies) are not nuclear reactions you want to study.
However, I also think you should not be in a hurry to work with a nuclear chemist or physicist. It is probably best to consider the advisor whose area interests you the most, even if it means waiting a semester or possibly two.
It is really best to ask the experts, but I try to help. I am not sure of many of these outlooks.