I can offer some thoughts, but it seems that the hospital you are using doesn't follow standard US protocols used in children's hospitals. For example, children are not given injections in such a way where it has to be explained. They are given a little flavored gas through a mask, and then the IV is placed after they have responded to the gas (usually by falling asleep). They bring in their lovies, like a blanket or stuffed animal, to hold while getting the gas. The nurses are generally of a personality that that is warm, caring.. Yes, children do sometimes get upset, but the protocol is designed to minimize anxiety and trauma.
I also can't think of minor surgeries that require two weeks of pain meds! Healthy children bounce back amazingly fast from surgeries. Much faster than adults. My elder had a tumor removed from her foot and was in a wheelchair for a month, and she was off pain meds within 3 days. I used to do outcomes research in ped surgery, so I know she wasn't unusual.
I think your matter of fact approach is great. Do not go into great detail about anything that could cause anxiety. If your child is indeed getting a straight up needle injection, then I probably would not mention it. You ask the anesthesiologist to use a skin numbing cream and then explain to your wee one that he will feel some cold and then a little pressure. Bring a lovey, favorite books, games, etc. and do lots of hugs and attention in pre-op. Don't let him see you cry (you will likely tear up when you separate. It is natural for many mamas to get some tears). Don't talk about post-op too much... You deal with that when it happens, b/c it is different for every kid. Also, your hospital's protocols will determine what some of that looks like.
If your child's mobility will be limited for days or weeks, you can talk about it some now, but most 3 year olds can't process too much of it. But it is worth starting the conversation now -- how long will be in hospital before going home, what the hospital room will be like, what kind of movies will we watch while resting, etc. You can buy some new puzzles, games... Rent or borrow new or favorite movies. This is not a time to limit screen use
. Your goal is to keep your little one on a good road to recovery (not tearing at IV or stitches, etc.), so if that involves a bunch of games on an iPad or something, you can worry about weaning him off of it later.
If the surgery isn't minor, you don't have to make a big deal about it, at all, but please don't tell your child it is minor if it isn't. It won't align with his experience and will be confusing. It will cause him to not trust you if he needs a future major procedure and could cause anxiety in that scenario. You just say after the surgery that mama is going to take good care of you. We have special medicine to keep you feeling as good as possible. You will get some treats (whatever that is for you...). We are strong and will be on this journey together. Many hugs and songs...
I think it would be worth calling the hospital in advance to ask about their protocols with children, especially pre and post op. Then you know what to expect and can be an excellent guide to your child. My children have needed several procedures/surgeries, and I used to work in a major children's hospital surgery practice, but I still make that call, and we go through everything again in pre-op with nurse, anesthesiologist, and doc. We are all on the same page and can work together to make things as minimally stressful as possible. For example, if my child needs to be taking in clear liquid by X hours post-op, I make sure that liquid is something my kid can tolerate, is acceptable to the nurses, and a bit of a treat to my little one (say, apple juice, or a Popsicle). I have also done a hospital tour to see the rooms and layout, if we were going to be there for a bit.
I hope this is making sense. My husband and little one are sick, so I have started and stopped this message a zillion times. I can hardly remember what I have written! I know you will do a great job, even if there are times that you are counting the hours until your wee one feels better! I wish him the best possible outcome and a speedy recovery!