The remodeled <A target="_blank" HREF=http://www.newholland.com/na/Products/impchart.html>New Holland Website</A> lists up to a 84" 951B rotary cutter as being appropriate for a TC40.
I run a 6' on my TC35D. I find that it strains the most when cutting wet tall grass IF I have the rotary cutter on its very lowest setting. Since my woods cutter has a solid metal rear skirt the cut grass cannot really escape and the tractor does slow down sometimes. Since I've raised the rear end of the cutter (and grass can actually get out now) it cuts much better. If I were you I wouldn't go smaller than a 6'. 7' would probably be about right.
I have a Land Pride 2572 (6') for my TC45D. The TC40D is about the same weight so it should handle it. I opted for the heavier cutter (as opposed to the 1572) for going through brush. A 6 footer is the biggest size I would use with the 3pt hitch. There are wider cutters that are drawbar or semi mount but you may find heavy mowing difficult with that high a power demand.
I'm running a 6' BH behind my TC45D. No problems with it, could go bigger, but would not result in a significant saving in time spent cutting. Besides, would cut down on my "Precious Seat Time!"
I have a Land Pride RCR2572 on my TC40D. It runs through almost anything. Watch your 3pt width.....mine was delivered from the dealer rubbing on the back tires.