Upvote:6
The Haimurubushi Hotel on the island offers:
Kayak rental. Based on my rough estimate from Google maps, the mangrove is about 7km/4mi away. That would be an easy round trip for an experienced kayaker, I think, but it may be a bit far if you are a novice. (Caveat: IANAK - I am not a kayaker, so please make sure you get more experienced advice before attempting something like this!) I don't know whether it would be possible to rent a kayak and transport it somewhere else.
A nature tour that includes seeing the mangrove.
I suspect there may be other options, as well, but perhaps not easily findable in English. There is a town in the southwest corner of the island, which has a hotel and other tourist amenities. I would not be at all surprised if it were possible to rent a kayak or other watercraft there. This would be much closer to the mangrove--perhaps 2km/1.5mi.
Update: there are also packaged day tours of Kohama Island that leave from Ishigaki. Perhaps you can find one of these that includes touring the mangrove.