Here are the problems and how to go about it:
1. The internal diameter of the shaft can vary from manufacturer to manufacturer -- sometimes as much as 2 mm. You cannot make this up with extra epoxy -- it will still oval out or not line up correctly and you can create a stress riser. If for some reason the shaft is aluminum, you've got a mess. I'll assume it's glass/carbon, etc.
2. The "spigot" (name for the internal sleeve) should be about 8 inches long, depending on the length of the paddle. Longer = more weight (but they're made out of carbon, usually) and more strength so you shouldn't need an external wrap of glass/kevlar/carbon on the shaft. If the spigot is too long, it'll interfere with the ovaling/indexing on the shaft, provided it's not an add on such as a shrinked wrapped indicator (then no issues). So measure the distance between the ovals -- I'm assuming since you said nothing about shortening the stick, you should be fine.
3. So, other materials. You need real epoxy. I prefer West Systems since it is very hard. System 3 is fine as well, but their product is a little softer and really works best on top sheets and sidewalls of skis. Do not use Devcon or Gorrilla Glue. Devcon can break down in constant water use and Gorrilla Glue expands. You're looking for something to hold it together and won't slip. There are other products out there, but West Systems is best for this one. (I was once teaching in Parkdale after assembling my paddle 3 days prior. A blade fell off while my entire class of 200+ pound guys were swimming through 3 rocks at 2000 cubes... Kind of embarassing)
You'll need spigot (sleeve, ferral, whatever your local shop wants to call it).
You'll need an epoxy thickener, such as resothix. You need some sort of template (other paddle at 15 degrees) or a protractor (to measure angle). Lastly, electrical tape and rubbing alcohol to clean up.
Hopefully the cut is clean. Rough up the inside of the shaft. Rough up the outside of the spigot. Fit together. Mark a halfway point on the spigot so you know how far to put it in. With epoxy on it, it's like KY so expect some more slippage. With the spigot in the shaft, set you angle (make sure the control hand it correct!) and mark the shaft with lines (3 or so) from one side to another. If you want, use 3 different colors so you don't think about which line it which.
Mix epoxy per instructions and add thickener (some people add thickener before the hardner is added, your choice.) The consistency should be like a peanut butter. Use enough thickener -- other wise the spigot will slip on the shaft.
With latex gloves on, lube up the inside of the shaft -- both halves. Put the spigot in about 2/3 of the way to your half way mark. (with how much epoxy in the shaft, blob it up and I twist the spigot on the way in to make sure it is covered.) Put some epoxy on the spigot coming out of the shaft. Carefully get the other half of the paddle on (watch the spigot so it is not excessively going into on shaft half or the other) and line up your lines. Do a quick couple of wraps (don't twist the shaft) w/ tape. Wipe down any stray epoxy.
Leave it alone. If you put it in the sun (heat is good for epoxy, it crosslinks it and makes it stronger) make sure there is no way for the blades to twist.
After a day, so if you can twist it in your hands -- I doubt you will but if you have epoxy failure, now's the time to find out.
Have fun, it's really not that hard.
So most spigot's are much thicker that the original shaft. If it's long enough, centered and put together with good epoxy you're fine. I have even used a hot glue gun with no issues.