I don't think there's a way to disable it (I wouldn't want to anyway - it has been very useful).
I guess there's a few ways to stop the log growing to an unmanageable level.
One option would be to launch the app via a small batchfile like this:
cd c:\arcade \programs\mamewah
del mamewah.log
mamewah.exe
This would give the benefit of always retaining the most recent log, but ensuring it never gets big by deleting it before each run. The downside to this (when I just tried it) seems to be that you briefly get an DOS window intruding., but you get the idea. This delete could be done in various places before/after executing mamewah, or at startup/shutdown.
Hope that helps!