If you stammer or make a mistake while speaking on the phone, it's okay as long as you get your point across. Don't judge yourself on whether or not you're perfectly charming, but whether or not you get your point across.
If you're being confusing, people will ask for clarification. It's not like you're leaving a voice mail. If leaving a voice mail, know roughly what you'll say ahead of time, but don't rush through it awkwardly.
The people who you talk to on the phone talk to dozens of people on the phone a day, and they have their own jobs, duties, and stresses. If you're less than perfect in delivery but the point is solid, they'll be happy, and even if you sounded like an idiot the whole time, they'll forget about it 3 seconds after they hang up.
Make phone calls at every available opportunity. Instead of looking something up on Google, call and ask on the phone. Get used to all kinds of phone interactions.
Find some way to connect to the person on the phone. It will break your own ice. If they state their name upon answering, use their name when addressing them. Ask them how they are today. Say something funny.
Write down how scary it seems to you before you make a call and how bad it actually was afterward. It's never that bad. Your own statistics will sooth your mind.
Make the call now. This way you can avoid putting it off and making a bigger deal out of it than it really is. Just dial the number, you'll still have a few seconds to relax before they pick up.
Good luck, and make the most of this experience outside of your comfort zone!