There is some paddling in the central part of Panama and around Panama City, but most (and the best) is in the western part near to Costa Rica. Also, if you are thinking next month, it is still the dry season and there won't be much running, especially in the central and Panama City area. There are some runs in the western part of the country that are good to do in the dry season. Of course, it can rain anytime and there could be something running. In addition, if you are in Panama City, you are only a five hour bus ride (or 45 minute plane ride) from the western end. It is easy to get around.
We won't be in Panama full time until the end of the summer, so I won't be around when you are there. Just to let you know, we are doing more than kayaking. We are also doing multi-sport custom trips and kids groups (camps, schools, etc.). We started doing that last summer. If you go down in the future with a mission trip and want to include other activities (rafting, hiking, kayaking, etc.), we would be happy to work with you and set things up.
In addition, we are offering service projects with our trips and can definitely organize and run a trip dedicated to service oriented projects. Some of the things we are looking to do are maintenance in the national parks, reforestation, clean ups, working in indigenous areas, and possibly some home building. We are planning on working with established non-profit groups already working in Panama to do these sorts of things.
Feel free to email me if you have more questions.