I figured, after a bit of headscratching and after Google came up with nothing but "don't do it" from the nannies out there, I'd share my findings here with my buds, since we like to mod stuff like put a different regulator in, etc. My reason was a broken wire right behind the strain relief (which is actually a strain concentrator, just that the strain is now moved back from the entrance to the case of the adapter).
NO, it's not usually super adhesives, it's a plastic weld, usually ultrasonic, that holds AC adapters together. Laptop and wall wart adapters can be taken apart or disassembled with some simple tools and a little care and eye/hand/ear coordination.
Just realize that the voltages inside can be lethal and if you don't know what you are doing, you can do a lot of damage to people or property, including cause a fire. In other words, you are on your own in doing this.
The "really sharp utility knife and/or chisel/hammer combo" method on the web might work, but I found a really nice way that causes little damage. First, check and see if you have some screws hidden under logos, stickers, etc. All the prying or chiseling in the world won't get it apart if it's screwed together and it'll be kinda embarrassing to discover this after you've carved a Mt Rushmore replica into your adapter plastic with that chisel.
I used an arbor press, but a vise would work just as well. Get yourself a deep socket, something like 3/8 inch or 1/2 inch (13mm for you metric people). It may be easiest if the socket does not extend to the corners, but rather, say half or 2/3 the length of the seam. Take a close look at the seam that runs along the "waterline" of the adapter. If you can figure out which half is behind the other, life will be a lot easier. If you can't it's a coin flip, and since it's busted anyway, you really have nothing to lose. Place the socket along the seam, just above or below it, ideally on the side that's behind the other in the seam. Now you'll put the squeeze on the socket on one side which, as a cylinder, will concentrate the forces just below the seam and nowhere else on the case, and the other side of the adapter in your vise or press (even vise grips may work, preferably the welding clamp kind with the wide jaws). You may also be able to do it with a c-lamp and no socket. You'll hear a cracking noise as you increasingly flex the plastic seam by slightly closing and opening your press/vise/clamp, which means you're getting the job done. Flip the adapter to the other side(s) and do the same. I only had to do the two long sides of mine.
With a bit of luck, it'll come apart to where you'll have most of the plastic intact and, using this method, the outside of the adapter won't look like there was a woodpecker party from all that chiseling. I have found that it's the cord at the strain relief and that soldering in a fresh part of the cord an inch or two back from the back of the strain relief works, but you won't have a strain relief anymore. You can get creative with reusing the old strain relief (I sliced along its length with diagonal cutters aka “dykes”) and use heat shrink tubing to hold it together. If you are replacing the cord, don't forget to slide the heatshrink on loose BEFORE you solder the wires onto the circuit board :-) Some adapters have three wires, one is used for ID...make sure you remember which wire went where.
Once you're sure of your repairs by trying it out, black electrical tape gives your adapter that ubernerd brag factor that you know how to fix stuff, you CAN use hockey tape to give your adapter a Canadian identity, or you can be stealthy about your skills and use ABS plumbing cement from the hardware store to glue it back together...just realize, if that cord broke once in a year or two, you'll be in it again in a while, which is why I taped mine. The last step is to slide the heatshrink onto the split strain relief and shrink it.