J.S.: Do yourself a favor and buy a Williams receiver peep sight and mount it on the back; the holes are already there, and are pre-tapped. Cost is about $35. You'll see your accuracy REALLY increase. A post front sight helps, too. I sighted in a friend's M-94 a couple of months ago after he had done this, and found that groups of under 2" were the rule (!?) from the bench with Hornady Custom 150g at 100 yards!!!
Don't bother putting in the tiny aperature; you'll give up too much visibility, and you shoot about as well with a ghost ring.
I would feel just fine shooting at well-defined, standing (preferably grazing) mule deer or whitetail at up to 150 yards with an iron-sighted rifle of similar accuracy. The whole point is, of course, to be able to use your M-94 without spending the cost of another rifle.