@kathymaynard Congrats on your first Mumsnet post!
First off, I'm really glad yourselves and the school have been supportive. This can be a difficult transition for the parents/school as well as the child, and so many people panic and end up on the wrong foot. It's good that within the household and at school you've got a good network of understand and support, that's really important for if other areas (such as the one you've posted about) end up being more challenging.
First off, it's worth remembering (both yourself and your partner) that people change their perspectives throughout their lives, so even if your parents' first reactions are negative, it doesn't mean they'll be negative forever. (I definitely found that as a young person coming out.) As you've said, your child is sensitive to people's approval when he cares about them, and that can make adjusting expectations quite difficult. He might not necessarily internalise that an initial bad reaction isn't necessarily a permanent one, so it's worth finessing the situation in order to minimise harm to him.
Depending on how emotionally mature your son is, you may want to consider talking through options with him personally and have him lead the way. Obviously you know your son better than anyone on this forum, so that needs to be on you to reflect. If you do think he would be emotionally mature enough to work with you on a "strategy", then it's worth starting that sooner rather than later.
Some possible options are:
a) him staying in the closet and being referred to with his birth name during the visit, agreed with him beforehand. This routes tension at the risk of upsetting your son and putting off the inevitable, but gives you a less time pressured environment to think through this issue. I wouldn't recommend doing this unless your son prefers the option, because it could lead to him thinking that you're not willing to stand up for him or put in the effort.
b) support your son in coming out to your parents while they're visiting. This means that you get to see their initial reaction honestly and (depending on your parents personality types) means the social pressure to be convivial will supress any of the harder conversations until a later point. Obviously, this is risky and could result in there being an argument at the picnic.
c) supporting your son to come out to your parents before they visit and be on hand to answer any questions. This means that their behaviour at the picnic is likely to be more pre-meditated and will give an indication of how they're likely to react in the short-medium term. This does mean that you're likely to get more sensitive questions in the intermediate period (e.g. about medical transition), but neither yourselves or your son should feel pressured to answer those questions in that environment. After all, he may not even be certain himself at the time!
d) he not come to the picnic, and make up a relevant excuse. This doesn't seem to be the best option given your son is keen to see your parents, but it's still possible.
Overall, it's really important to communicate with your son about how he wants to go forward. You deciding for him without talking it through with him could be interpreted as infantilising, as if you don't trust him, and as an invasion of his privacy. Obviously you want to do the best for your son and protect him from harm, but this is his life and he needs to feel you have confidence in him.
Sorry this is very long! You are facing a difficult issue, but you have already built a really strong foundation for his resilience and future. If you haven't already, I'd recommend joining a "parents of LGBT kids" group and seeing what local youth LGBT groups are options for him. This situation may prove really challenging for him, and having a space for him outside the family will allow him to explore his feelings in a safe space without feeling as though he's disappointing you.
Best of luck to all your family!