I've got a late 70s/early 80s Schwinn 3-speed at the house right now with a spiderless Sugino crank. In this case it seems that it is not like a BMX or single piece crank but rather like the drive-side crank and chainring are one piece ... or at least might as well be since I can't figure out how to take it apart. If it is old looking, check with the folks over in the classic/vintage forum or take it to your local bike shop that has the oldest mechanics who might remember this set up.

That being said, as long as whoever set up the rear wheel used the right kind of loc-tite, getting your cog off shouldn't be a big deal. I'm not a strong man and I got one off with just a little elbow grease a couple of weeks ago.

Or, if you have some money to invest, a new rear wheel with a fixed hub would be your best bet (IMO). That way you could get a bigger cog and have the peace of mind that comes with a "proper" set up. (Note: no offense to folks running the loc-tite hubs ... some of my best friends do this )