I will shoot in the dark as to why I wouldn't think that the greenlee cutter won't work on wood. I will guess that it may splinter the fibers significantly. Seeing how it wasn't designed for wood, I think you should try it on a thin piece first to see how the wood reacts.
The best advice that I can give about cutoff wheels is not to be in a hurry! Skim the cut line with it a few times, and watch out for when the disc cuts through the metal. Find a position that you can steady your hand as you work the cut, and remember to stay 'straight' on your cut. If you start to arc your cut, that's the most likely time for the disc to grip the sides of the cut and take off.
As to bit geometry, make sure that you have a sharp bit, and that the cutting angle of the tip is 85 degrees. More importantly, don't use a bit with outrigger teeth as these are designed for wood only. The side flutes of the bit don't matter as much, but there are some designs that are raised and really like to grip the sides of the hole, making the bit climb into the hole quickly. I suspect these bits are designed more for drill presses that you would have the object clamped down in the first place. In some cases, I would use a cutting wax to help the drilling process, but no for aluminum. Brass seems to be it's own lubricant. Steel may need a little more patience to drill.