Birthdays are sacred. I would do everything possible NOT to mix up birthday celebrations with discipline. don't do it.You don't say what the misbehavior is, so it is hard to give advice, but try to keep your consequences brief and related. If he mouths off to you, he loses TV time that night. If he refuses something you have asked him to do (like clean his room), you don't do his laundry for him today. It is important to keep the consequences simple and unemotional. And equally important to sit down and talk to him, "It seems like something is really upsetting you lately, you seem angry with me all the time. Do you want to talk about it?" If he refuses, just say, 'When you are ready to talk, let me know, and I will make time to listen" I think it is important to be honest like that, because as a single parent you are probably very busy, and it may not be apparent to him that you have time for him. I used to give my son a laminated board that he kept on his bedroom door, and he had several pictures he could put on it (we made them together using the PECS (picture exchange communication system) system from Don Johnson. We were making a communication book for his disabled brother, but we just took some of the pictures to make a communication board for him). The pictures said, "I need someone to talk to." "I need attention", "I need help with homework", "I need money for ____" etc. and he would put them on the board when he wanted something. I would check the board every day to see if he wanted anything from me, and make sure I made time to give it to him. We still had a tough time communicating throughout his childhood, because his brother's special needs continued to be more urgent, but at least he knew I was trying.
When I say Birthdays are sacred, I mean, you don't want to do anything to take away that annual opportunity to focus on valuing and honoring him. It's not like you can make it up to him next week, once it's gone, it's gone, and it is too big a thing (even if you are only planning a simple celebration) to take away as a discipline. So don't threaten it. I only did it once, I had a sleepover planned, and my darling pre-teen son told me to "Go back to the Hell you came from", so I called all the friends and told them not to come. That was my limit, I didn't want him to think he could say something like that to me, and still have me knock myself out putting on a party for him. But to this day (he is grown and in college now), he is still hurt by that cancelled birthday party. I wish there was some other way we could have handled that. So my point is, don't let things escalate to that point. Keep discipline simple and related, give as many complements as you can, and keep big celebrations such as birthdays and trips to Disneyland off the bargaining table in discipline. Sometimes kids who have problem behaviors feel like they can never be good enough to deserve something special or good. You don't want him to develop that self image, make sure your son gets more compliments and expressions of love from you than criticisms or reprimands. Make sure your rules are clear and simple, go over them with a friend to see if they are reasonable, and be consistent about enforcing them. Limit TV and video games to about an hour a day (combined), maybe two hours on the weekend. Have other fun things to look forward to, even if it is walking the dog together, or taking a bike ride. Or listening to him read, or you reading to him. We did this every night all through elementary school, and even a little bit in older grades when he had a lot of reading to do and was overwhelmed. We would read the novels together and talk about them.
We always had simple, home grown parties, one year we made pinatas shaped like Pokemon, one year we painted targets that we fixed to bales of straw and had archery practice with home made bows made out of pvc pipe. Your idea of taking one friend to the river sounds good. If you are taking more than one friend I would definitely bring more adults for safety. In fact, whenever there is water we always had one adult per child. Good luck, remember, you became a parent because you wanted to love and share your life with a little person. Don't lose sight of that long term goal in the day to day problems.