I ask the same question about every couple of years myself. If the broadhead is sharp and you hit the softball kill area...anything works. I've killed 'em with two blade stingers, two blade eskimo's etc.
That said, its hard for me to be consistently that accurate unless I get them very close (like 5 yards) so I use a string tracker. It's the only thing I use a string tracker for but I would now feel handicapped for recovery. I had a 'bad' year a couple of years ago that made me change my setup a bit.
I now use the 2 blade Simmons Landshark as its over 1.5" wide. I'm shooting 52 pounds but I have a short draw length so that's as much head as as I want to try to push through a turkey.
Your 40 pound weight is some consideration in all of this. If you shoot a heavier arrow and have a longer power stroke you should be able to shoot anything you want... in terms of a larger had.
I would definitely consider a string tracker. A bit of a pain, but if you aren't going to shoot a Bullhead type broadhead, I think its a neccesity