In this day and age, I find it incredible that someone would demand a paper-based, snail-mailed cover letter and CV. I guess some old-timers may still work that way, but my guess this is just to encourage people from email bombing them with bad application materials. If your materials are good, I think electronically delivered materials would be fine. If you've narrowed down the list of labs your interested in to a half dozen or so, you may consider asking your current PI to send them personal emails to let them know to expect your application and to say a few nice words about you. This will probably increase the chances that your email will actually be read.
Also, make sure to follow up at least once, about a week later.