Yeah, my EDC's are my razors. Using a two-blade disposable is a little "smoother" feeling, but not by enough for me to consider it more comfortable--or more like the knife isn't rough enough for me to call it uncomfortable. The shave I get with each is equally close. They're both incomparable to an actual straight razor in both smoothness and closeness of shave, but I feel a lot safer using my EDC than a straight razor.
The first time I used it to shave I was thinking of the Crocodile Dundee scene as well. Thought I'd give it a try, and it worked so well that I prefer using it over safety razors now. Having a knife with a good belly really helps me shave the corner of my lips, and it also gives me a weird prideful feeling. If I'm just in a hurry though, the safety razor has its advantage in that I don't need to be careful with it, but I don't like sticking my tongue into my cheek to get the parts of my face I need shaved in contact with the flat surface of the safety razor, so when I have time for a "nice shave", I use my EDC.
I never thought the Crocodile Dundee scene was real, and always sharpened to that goal as if it was something I'd never reach. Now that I've found it's not so far fetched I'm working on getting an edge I can split a falling hair on like Elemer Fudd; I think that will take longer.
I only shave about three times a week to take care of stubble mostly though. However, I had my friend try it out. He shaved a little off his face and then his entire leg. He use to swim so he has experience in shaving his leg and says it usually hurts more than his face--I guess face and leg hair being different occurs in different ways as well. Either way, I don't know how fine or coarse our hair is, but it works for either one of us so I'm not sure it's just a matter of only fine hair being shave able.
Both EDCs I've used for this aren't very acute either. One was 30 inclusive, and the other is 40 inclusive. I've noticed the 40 inclusive has a little more "drag" to it, but it doesn't really qualify as uncomfortable or rough. With shaving cream or lather it's all the same, the only time safety razor feels just a modicum more comfortable is when I dry shave.
Oh, and I just use a 1000 grit waterstone and a strop with green compound.
I'm not really sure why so many people think of it as if it's impossible or something. I think most people are just comparing the shave to their multi-blade saftey razors or their straight razors, and if you already need that for a shave to be comfortable, there's no way you'll be able to use a knife. I think that most people that dry-shave with a disposable saftey-razor could shave with their EDC though.