Orienteering might be worth looking at. You don't need to run, esp at the smaller events, you can walk or joggle a bit. Some events are on very even ground, others in woods or some open acess land. It's a case of pick the events that suit you. It really is good fun, esp for you as you enjoy adventure racing.
Other than that, golf, but then you could just take up hiking or long distance walking. Be much more fun.
Swimming you can do as and when but it can be a bit expensive, no more so than running though, less kit just more up front money each time you swim. I'm lucky and can swim in the sea for free in the summer when they hike the price of the pool, in the winter the pool is cheap.
Gym, or exercise at home. It's not really sport and you don't get medals but I don't think any other sport gives you medals just for taking part.
Extreme ironing.