Rhyta

Hi! I'm looking for some advice. My advisor wants me to send a research paper I've written to some of the major researchers in the field and ask for feedback. I am scared stiff at the prospect. I'm scared of being annoying, wasting their time, or sounding conceited or stupid, or all of the above. Does anybody have any tips on how to word my emails so as not to offend (or make myself a laughingstock)?