Amy, et al - well to start with let me clarify couple things. I incorrectly mentioned my parts book TC137. It's actually TC-157, but it's only for tractors. Now, I do have the CPE-2 parts book which is for "Equipment for Cub Cadet Tractors" so we're off and running.
According to the CPE-2 the bearings for a CW36 is Part No. 475-538-R91 which appears to be an assembly with 2 sets screws. So it must come assembled with the flanges and some type of locking collar, and you add the 5/16-18 x 3/4 bolts(3), or for some reason you add 5/16-18 x 1/2 bolts(3) (maybe they are different depending on which end of the auger they are mounted to). I also checked the CCC parts link and it still lists the same bearing assembly. In fact, the picture on line is just as poor as in my CPE-2 parts book.
Next I looked at the shaft, and I see they list a tail shaft and a drive shaft, both shown as the same item in the parts diagram, so the one with the sprocket must be the drive shaft, and the other one must be the tail shaft. Again, the diagram pic is terrible and doesn't show any detail. You have to look at the large sprocket in another diagram, and it's separate and not shown with a shaft, so it may not necessarily be welded to the shaft and you'll have to figure that one out. It also shows a serial number split where the drive shaft part number changes. Maybe this is a welded and non-welded version, it doesn't say.
Next I did a little cross checking, comparing the bearing and flanges with a QA42A and discovered the following:
Bearing No. 475-698-R91 replaces Bearing No. 475-538-R91 (your bearing) by adding 455-102-R91 Collar, and 462-360-R1 Flange(2). So, based on this you may be able to re-use your flanges and just get yourself the bearing and locking collar. (The PTO and snow thrower auger bearings are not the same, and it's very unlikely they can be interchanged. But I've changed several and it is the same). If I can find the standard bearing number I'll repost with it, or maybe someone else can tell us the bearing number marked on the actual PTO bearing they may have recently replaced (and you can get one at a good local NAPA store with the collar). You'll still have to see if the bearing will fit snugly between your 2 current flanges, and then see if locking collar can still fit onto the bearing when the flanges are in place. If not, you'll have to buy the new flanges.
I realize this doesn't help get your drive shaft removed. You'll have to figure out a method to pull/push it apart. Hopefully this is still helpful.
I'm also hopeful the rest of the thrower is in good shape. I've never actually known anyone to use a CW36 or for that matter a BB36 which is very similar. Before putting alot of money into it you might want to start looking for a QA36 or QA42 version. Your thrower has a shorter auger and the sides of the housing are winged out to measure 36. The QA's have a bigger auger and no wings on their 36 or 42 housing. I don't recall which tractor you have but if it's 1x2/1x3 or older then you'll have to figure out a method to bolt it to the frame. It's not a direct bolt on, but can be adapted. Let us know how you make out.