The thing about autism is that it's not about degrees, it's about the child's particular issues. Each autistic child has his/her own unique set of issues. Each issue is likely something shared by other autistic kids but the issues all together combine to make a unique child. Your cousin needs to really think about her child's particular issues. Is he a sensory seeker or a sensory avoider or a combination of both? Is there a particular sensory input type or particlar sense that is significantly more sensitive than others? What are his common meltdown triggers? Is he likely to run? Does he have any gross motor skill or fine motor skill issues? How is he with costumed characters? Does he crave his routine? Does he need to be prepped in any way for the trip? And so on and so on.... It really does come down to his mother understanding his needs. Whatever his needs are at home, those need to be doubly taken into consideration any time they go somewhere he's not used to and yes that includes the happiest place on earth.
The Passporter book Open Mouse is an extremely helpful book. I read it before our frist WDW trip with our autistic daughter. The advice in there was unbelievably helpful (we also needed the sections on food allergies but the sections on autism were just as helpful).
Unless he has some kind of mobility or trunk strength problem, I don't see why he'd need a wheelchair. Something that some parents of autistic children do find though is that a stroller is extremely helpful even beyond the age where kids typically use strollers. The stroller not only helps with fatigue (something that can definitely lead to a meltdown) but also it provides a safe place for the child to get a sensory break from all of the stimulation around the parks. If they no longer have a stroller or don't want to lug it on an airplane, they can always rent from a company like Orlando
Stroller Rentals. Some parents find that they need the stroller right in the lines either to keep their child from running off and others find that they need the stroller right in the lines to help force a perimeter around their child or to give that extra sensory break even in lines. We've never found a need for this but many parents do. Again, you really need to know the specific child's needs.
His mother will need to be able to explain her child's issues to the CM at Guest Relations in order for the CM to provide the appropriate accomodations.
For us, I've found that one of the best tools we have in addition to sticking as close to our at home schedule as possible (getting up, eating, going to bed type things) is a really good touring plan. Planning using TourGuide Mike has made a HUGE difference for us. The accomodations that are given typically are only provided for the person with the disability and up to 5 other guests. With a larger group like yours, you'll really want a good touring plan to make this work really well. The touring plan will also help you to be in non crowded areas of the parks between the rides. There are no accomodations that Disney can provide for these areas (though a stroller might be a big help for these areas).
If you have any specific questions, please feel free to ask.