Irismarie,
You have hit on the one thing that I too have struggled with. Unfortunately I don't really have an answer and if I am using my netbook I have to be seated with it in my lap or on a table. This works at home if I want to talk with my family, I just sit in my recliner and I have a large clipboard that I set the netbook on. The clipboard (I have removed the clip assembly) is big enough that it sits comfortably on my legs and is large enough for my mouse.
I don't know how it would work on your lap on your wheelchair, I imagine it wouldn't be very stable or secure. Does your chair have a tray attached? If it does you could attach the netbook to the tray with some heavy duty velcro which would hold it fine. Just don't plug up any vents underneath. I am in the process of getting a loaner pwc and I hope that I will be able stick my netbook to it somehow, I will let you know about that, I will have to put my inventor hat on.
You are right, it is too heavy to hang around your neck although I have thought about it. I have a friend who told me about some kind of tray thing that you wear and you have a tray in front of you but I haven't found anything like that and I don't know a person would type on the netbook with it so close anyway (to say nothing about lap puppies getting in the way!:shock
Of course these problems are why I also have an IPod which I can put into my pocket. It is ok because it is very portable but it does require at least one steady hand to type on the small touchpad and I cannot be as fast as on my netbook.
I have used my netbook in the sun and haven't had a problem reading the screen but I am more of a shady kind of guy anyway, if you want to find me on a beach look for the umbrella or shady tree.
Sorry I couldn't be more help, I will let you know if I have any brainwaves.
Barry