I think there are several choices here. You can perform as if you have psychic abilities, as if you are demonstrating psychic abilities or as if you have abilities other than psychic abilities (reading body language). I think you can tell the differences with how you script the introduction to your show.
For a claim of psychic abilities:
Ever since I was young, I could read people. I could tell their mood and sometimes guess what they were thinking. Often, I would just seem to know the next thing a person would say. My mother said I had good intuition. But there was more than that. I would get a sense of something that would happen -- a premonition. Sometimes it was a general feeling that something good or something bad would happen. Sometimes it was more specific. As I got older, I started reading more -- everything from studying psychology and neurology to studying psychics and the occult. I wanted insight into how the human mind works and to understand how much we don't know about how the human mind works. Tonight, I want to share my insight into what the human mind is capable of with you.
Notice how you don't come out and say you have ESP or physic powers. If you said you were psychic, the audience would automatically reject that idea and you would lose credibility. By leaving it vague (without a disclaimer), the audience can draw their own conclusions. You also set up your "powers" to know what people are thinking and to know things that are going to happen. Each performance piece in the show should relate to one of those powers.
As an aside, I don't think you need a disclaimer. The "I'm not a psychic and all this is tricks" line kills any believability and people just end up look for methods. It trivializes what you do. The "I'm not a psychic but you may not believe that after you see my show" isn't much better.
For the claim of demonstrating psychic abilities, this is the introduction that I've written for a show I'm developing (read it using the narrator voice from the Twilight Zone):
What you are about to see is a demonstration of the paranormal. You will see things you cannot explain, experience things you do not understand, confront things that you will refuse to believe and find possibilities that you never thought existed. Tonight, I invite you to explore the distinction between what you know to be reality and the potential of the human mind.
Now, you can't follow this introduction with a tossed out deck routine - the show has to live up to the hype. As with the first introduction, it leaves the audience to draw their own conclusions. This allows me in my show to work on exploring different "powers"' and to have the audience participate in the demonstrations (I am actually trying to develop a piece that has an audience member act as a psychic to solve a murder mystery).
The "reading body language" introduction would be something like this:
I consider myself an astute observer of my environment. Watching people, you can discover patterns that are typically only noticed by our subconscious. They say you can't tell a book by its cover, but I've found that I can learn a lot about a person through a momentary interaction. We all do that to an extent. We can tell if someone is lying, if they are afraid, if they are upset or if they genuinely care about something. What would happen if you took those feelings or those senses about people, combined them with a knowledge of human nature and consciously analyzed people's voices, reactions and non-verbal cues? Tonight, I hope to answer that question.
Again, it is the suggestion of powers, not the claim. As with the "psychic" introduction, you start with things that people can relate to and you claim to be able to do the same thing just at a higher level. As with the other introductions, you effects need to follow the claimed powers.
Also, how do I perform as a psychic without coming across as silly?
Don't trivialize you performance pieces. Give them the seriousness they deserve. Care about the people you are performing for and the people who assist you. Don't use playing cards. Don't do magic tricks (like a floating table). Develop a character that is interesting. Select effects that fit your show and your character.