Just for a second, consider a different job, and think what will happen if everyone start doing that. If your doctor does that, a truck driver does that, if an engineer does that when building a bridge.
I'd say, you should be honest and direct. Just tell your employer/manager: I don't know that, and I need x amount of time/resource to learn it if we need.
You shouldn't fake it. They should know the real cost, the actual capacity. Either they will support you to learn it as part of your job, or they know that it works better if they think about alternative solution/design base on actual capacity/resource.
Nobody can blame you for not knowing something as long as you are willing to learn and they are willing to support you.
"fake it till you make it" also doesn't help you with your stress condition. it will make it even worst as you and your employer don't have real expectations.
Don't build that kind of culture in your job market and society.
