So my question is, how can we deliver the message that someone does not perform to our standards and that the specific examples if repeated would have a big impact on the performance evaluation without making the individual feel threatened?
You cannot. Because that is exactly what it is. A threat. "If you continue to do X, I will do Y, and Y is bad for you."
What you can do is give the person a chance. Be constructive. What you have told us here is that you plan to tell people what they do wrong, specifically and that they should do better, or else. What I miss in there is a plan forward. A positive, constructive plan how to get better.
I don't know who you manage or how they could improve. But the most damaging thing you could do is tell them they are doing badly, not show them any way forward and then threaten their livelihood.
I had a girlfriend once who was totally devastated after their boss told her she would get a bad performance review because she did not copy files fast enough. Yes, that was back in time where "files" meant a stack of papers in a binder. The point is: she did not know how. She would gladly copy faster, I mean it's no fun copying papers, the faster it's over the better. But there was only criticism, there was a threat, but there was no way out. Nobody stepped up to teach her.
So for each person you manage, tell them what you want to improve and tell them who can teach them. Then give them time to learn it.
Show every employee a realistic way to reach your goal. "You did bad" is no feedback that would enable anybody to do better next time. "This was not good, here let me show you how to do better in the future" is a solid way to turn their performance around.
Since you said you already have the personalized suggestions how to improve:
If you want to have this conversation with less of a threat, then do not threaten. "Get better or else I'll do a bad thing" is a threat. Don't lead that way. Lead with the current (probably bad) performance as a given and give them the options for improvement.
If I had to rate your performance now, I'd had to give you a 2 out of 5 stars. But the official performance review is two months away, so I have compiled a list of improvements for you to get a better review then.
Is a lot better than
If you don't do these things here on the list, I will have to drop your performance rating by two stars.
One is a direct threat, the other is an offer to help and an opportunity to get better.