HayleyK - I suspect catesmum doesn't use armbands because her child's shoulders and the rest of her body will sink below the water, while only the floats and the tops of her arms remain on the surface... That's what happened to my ds1, who is hypotonic and hypermobile, when we tried armbands on him, because he is so incredibly loose jointed around his shoulders! A float jacket was much more successful.
Swimming, trampolining, soft play areas, walking, pedalling a tricycle are all things that are worth encouraging your child to do (tricycle pedalling may take a while - my son just couldn't muster up the force to move the pedals for quite a while, unless on a totally smooth, flat surface). Later on, activities to strengthen the shoulders and upper body help with learning to write (for which you need good joint stability and strength). Writing on a blackboard, so that you have to have your arm up in the air to write, helps. So does wheelbarrow walking, stirring things, doing playdough, etc.
My son is now 4, and can run, jump and skip. He can also write - he used to be unable to apply enough pressure to make a mark with a pencil. He still has very pronating ankles and still finds stair climbing and descending quite hard work, and bicycle pedalling extremely hard work, but he clearly will get there in the end - he just needs to strengthen his muscles a lot more than most children to compensate for the loose joints.