I definitely understand your fears. I joined the gym on Monday just gone. I was so scared that I would be going on the treadmill and everyone would be looking at me and judging me. In reality, I went in, everyone was doing there own thing and nobody even batted an eyelid! I now walk in and just go straight to the treadmills to start my workout. Nobody notices. So my fear of working out around others is slowly decreasing.
You know this person so I think since you know him from coming in and out of where you work, you could even explain to him to go easy on you at first! You would really like a trainer, as you said! And to be honest, if you don't get over your fear now, you will find it harder later down the line. I would advice you to go and give it a try even
If you don't like it, or are too uncomfortable at least you can say you gave it a go. Just tell him about how you feel about your fitness level first.