When our 16 year old nephew was fighting cancer several years ago I also thought of sending a few packages. After the first couple my in-laws told me he began to look forward to mail time every day to see if we had sent a package. That's when I realized that having something to look forward to was as important as what was in it. Think about breaking up whatever you decide to send and send each thing by itself over a period of days. (I know it's more expensive, but if this is a long battle, small inexpensive things will be fine).
When I did this for my nephew I was working full time and getting to the post office was hard. I approached our local Mailboxes, Etc. store and worked out that I would bring 3 or 4 packages by on Saturday, pay for postage and then we would mark which day to send it - they would then mail them every other day or so for me.
You are thinking of all the right things to send. My nephew was in the hospital a long time and in addition to your suggestions he really enjoyed things we would send to decorate his room - a string of heart lights for Valentine's day, markers for mirrors and windows to leave messages, glow in the dark stickers to look at when he couldn't sleep, drawings from my kids, photos of family & pets, tape recordings of greetings from us (we lived on different coasts), books on tape (depends on the temperament of a 3 year old - but you could record short picture books in a friend's voice and send both book and tape), and gag or gross gifts to try to fool or gross out the doctors and nurses. His favorite was a fake cast kit we found - his grandma helped him cast his arm and he enjoyed fooling everyone all day.
We also sent a few food treats he was allowed to have (we always checked first). For food items he also liked the silly or the gross - think gummy rats and edible paper - but again, it would depend on the 3 year old's personality.
Several years after my nephew's illness, my own son was in the hospital for 5 months and I experienced from the other side how important little gestures can be and how important it was to have things to look forward to. Even if his family is too overwhelmed to thank you properly, know that what you are doing is an extremely kind and thoughtful thing to do for them and that it will make their hard days easier.