For regulations, it depends on who made the regulation, and how it exactly reads. I'm not familiar with Green Lake. Past electric motor only regs have disallowed gas motors from being on the boat in certain cases. Little surprising a lake like that doesn't want pontoons at least, if not jet skis, jet boats, speed boats, wake boats, etc., etc.
If you haven't searched regs by county in the
DNR Fishing Guide I'd recommend that. I don't recall seeing anything in there, but there's too much to remember off the top of my head. These types of rules are often a local ordinance or rule that might not be in the guide. Some of these local ordinances can be tricky to track down.
dartag might know something about the lake as it's attached to his Union Lake by a small channel, ditch or stream. Don't see a public access and don't recall anyone talking about such. Looks like very shallow edged with pretty deep water / drops a little like Union Lake, but without the more complex islands and ridges of Union.
Looks like the channel is navigable most of the way to Union but under the last bridge near Union becomes too small for a boat. Not sure you can get under that last bridge. Maybe a kayak... float tube? There's probably a ramp or ramps somewhere on the lake, but nothing with parking that sticks out. Looks like the high rent district. Hard to get public access on those public lakes.