Emailing Derm PI for research with a project already in mind
By - switra
No that's absolutely fine - the only thing I'd say is don't tell them what they will be doing - they're the supervisor and it's for them to decide how they supervise, plus you don't know what supervision you may actually need so don't snooker yourself.
Send a brief email with a top level description of the proposal (maybe attach a slightly longer proposal but not more than 2 sides) and ask if they would be interested in supervising it.
As for phrasing I'd do something structured along these lines:
I'm a student in year X of my Y degree. I'm interested in doing research and having read about your research, I was wondering if you would be interested in supervising me. I have had an idea for a research project looking at Z.
I would be very happy to discuss further or get your feedback on the proposal.