How to have uncomfortable conversations
It's uncomfortable for most people to get into a negotiation. It's uncomfortable because we rarely get the chance to do it and we're worried about making the counter-party angry.
If you're converting your job into a 1099 role, for example, you may have to have an uncomfortable conversation with your boss about leaving the company, your billable rates, etc. You will need to ask for what you want and not give them everything they want.
The way to make it less uncomfortable is to do the following:
Prepare
You should know what specifically you're asking for, how you'd respond in different situations, and practice your scripts out loud.
When I prepare for job interviews I literally write down stories and scripts and try to rehearse my lines out loud without looking at my notes. I look like a crazy person if I'm doing it outside. BUT, it pays off.
The act of preparing will make you feel more confident and give you the right energy and confidence going into the conversation.
Reframe
Don't think of it as an awkward, adverserial conversation. Think of it as two professionals trying to hash out a working arrangement that works for both of you.
Ditch perfection
There will probably be awkward moments in the conversation. No big deal. Expecting perfection will just make you more nervous.
Did you ever call your elementary school teacher "mom" on accident? Everyone laughs for a minute and then moves on.
As long as you don't call your boss or the program manager mom you'll be fine. And even so, that would make for a a hilarious story.