Well, I'm not sure if this is even possible, but if you're really serious on trying it, I have an idea. WARNING: I am not a computer expert, so if you follow my advice it is at your own risk. I'd actually recommend not following it, but anyways, I digress. First save the folder Local in (default location) C:\Program files\Auran\TRS2006 to a disk or separate folder. Then find the files assets.tdx and/ or assets.bku, which might be (might also not exist) in the cache folder and put them on the disk and put them with, but not in, Local. When you put in your new simulator, save the files to their appropriate locations. I doubt any of the stuff in it that are exclusively for TRS2006 will work though, and there is a good chance it might crash your computer. Again, follow this at your own risk, or better yet, ignore it. Hope all works well if you decide to follow.
If you select each route for archive and tick the option to add all its dependencies you can then archive the route. Then when you re-install you can add that archive to your archive list and restore it. Although I haven't needed to restore them yet (famous last words I expect!) I do this for any large route I download such as George Fisher's.
Both methods stated above will work, but bigboy4010's method may be quicker/simpler as you only have to copy two/tree files instead of packaging up all of your content.
Copying the local folder does indeed work. I've done it many times and I agree that it's probably the quickest method in this case. I'd also suggest copying the entire folder to a CD or DVD so that you have all of your content backed up in case of emergency.