Don't do something that you don't want to just because you're pressured. Plenty of people wait till they're 18 to get their license. Just don't let it cripple your experience; you'll probably need to be confident with driving a car at some point or another.
It's cool that you can drive your moped :3 And they're really handy, but if you need to go on a long trip, your moped won't be the best choice. All I can offer as far as advice is practice driving until you're more comfortable with it. I've been driving with a license for 2 years and I still really dislike driving, but most of my hatred for it has subsided :3
From personal experience, there is no polite way. Usually, when parents want their way, they'll get extremely butt hurt if they don't get it. If they're the open minded type, you could calmly express your fears to them. If not, which is most probable, I'd get your license anyways just to shut them up, and just not drive anywhere. But I'd still bring up your fears and stuff if they expect you to run errands or something.
There's no point in waiting, no matter what path you chose. Just get it over with!