Unlikely that it is the battery, just to let you know.
Need to test the rectifier FIRST, and if it is good, the regulator would need to be replaced (note- as suggested earlier, this one is NLA now, meaning you're hunting leftover or used parts).
While I have not ever done it on THIS engine model, I suspect that the later-style regulator/rectifier would WORK (slightly challenging to mount, but should functionally do the job).
Have used it on several other "non-Merc" engines over the years with decent results.
WOULD require some wiring work and at least a moderate knowledge of the workings of a stator-type charging system.