What you are planing on doing in the bathtub is the way to go. Everyday a little bit so your baby boy can get used to it. The shaking was probably from the stress and if you have your AC on real cold he might have been shivering from that too. I turn the AC off for a while until the babies are dry or I use the hairdryer on the low heat setting. I also lay out towels on the floor b/c thay love to rub and roll on them.
When I got our new puppy I let him look at first what happens to the others and then I put him into the tub while his big 'brother' got a bath. That way he saw that it is survivable...LOL... Since you don't have another pup just go slow with baby steps. Same with the brushing. I started out with a very soft baby brush and we kind of just played until that thing lost it's dangerous smell and look. A LOT of treats also help! Now at 7 months he enjoys being brushed with the great pin brush from
Chris Christensen.