You need, first, to ascertain the exact model that you have... If you open the bottom (inside) section of your A/C unit, you should be able to find a silver label (silver on most that I've seen) that will list a whole bunch of information and one of those tidbits will be the model number that is very long and rather obtuse; an example would be 520310.501D (this is for an example only, yours will be different unless I hit it on the nose accidently).
The tag you are looking for is 99.9% of the time viewable from inside the trailer (where it is protected from the elements), but, if you can't find it from inside, you may need to go on the roof and pull your existing shroud and look for it (not likely though).
Once you have the model number, you need to go to this site:
Dometic Parts
You mention two different type of A/C units in your post a Duo Therm and a Brisk Air...basically two different type of A/C units manufactured by Dometic and that may be part of the confusion. Since I don't know which type you actually have, you'll have to search the Brisk-Air listing and the Duo-Therm listing for those A/C units until you find that model number. Once you do that, and find it, you should be able to find the part number for the outside shroud. To narrow it down a bit, if your model number starts with a "3" it is most likely a Brisk Air and if it starts with a "5" it is probably a Duo-Therm. Once you've located the number, if you click on it, the link will open you up to the parts listing for that model number; another example:
Sample parts listing
The above should get you the information you need to order the proper outside shroud for your particular model...
