No worries. I usually use the 40/45w panels for science projects because you can come by them easiest. I find them on CL a lot. I'm assuming from peoples old RV charging setups, and they stock them at orchard supply. I think the regulator will work as long as it holds up to the incoming current (might not take that high of voltage without pooping the bed). Do you know what the lowest wattage 12v LED is that still has a color temp of 5000k +/-?I'm not trying to tell specific people what to do. I was just giving general advice WRT a small solar lighting system, as you were dc (by the way, even a 3 or 4 watt LED 12V light can provide enough light for a coop if you get a good efficient one). If you have a 40 or 45 watt panel laying around, it makes sense to use that, but if you are buying one, you really don't need that much to run lights and you can save money by buying a smaller one. Along those lines, your battery will wear out much much faster with a simple cut-off type controller. And, if you don't the right controller, your battery could overcharge to the point where it heats up/starts venting Hydrogen... the car alternator regulator could work, but I would test it very carefully.
I was in Central America for a service trip, and one of the volunteers at the local organization we were partnered with had put together a wind turbine using basically scrap wood, a car alternator, some fins from a fan, and a bleach bottle (the bleach bottle was the turbine housing), and a hinge/weight on a stick to tilt and protect the turbine from high winds. He ended up having to re-wind the alternator to get the right voltage/current characterisics for local average windspeed, but in the end he had a working turbine that generated about 40 watts that he had built almost entirely from junkpiles. Really made me drool.