I would probably manually update to 2.06+ and then see if Comfort Update works.
In any way, for manual update, I probably would update in steps and I wouldn't skip any major release. Just in case.
Also, with such an old installation, I recon it isn't used that much? Maybe a solution would be to set up a totally new and clean install of the latest 3.x LTS release (if you don't have many surveys that you still need or if you don't have a ton of users, which you would have to create new one by one).
I did the manual update to 2.06+ Build 160129, and the front end seems to work. However, when I try to log into the admin area, I get a 500 error message.
Weird, but a 500 error is usually do to some problems with the server itself. What version of PHP/MySQL are you running? With such an old version that hasn't been updated in about 7 years there is a good chance that the server it is running on is old "slightly" outdated.
Maybe the fresh install is your best solution for the moment. Your "mumie" is almost 7 years old now. I doubt anyone here has such an old version running (I honestly hope so!) to check things.
I don't know your setup, but I would probably "cut" my losses and just install LS 3.x LTS on a fresh server with an up to date setup, to be prepared for the future. LS has come a long way since 2.00 and there have been a lot of improvements and changes since 2013.
If last, is there a way to cancel the CU key in order to not have expire without using it?
I instantly hope that you will actually use it, once you have a more modern version running. There are always minor updates and bug fixes, so the CU key will not expire without using it, as long as you don't wait another 7 years, to do the next update.

(sorry, it was just too tempting...).
But honestly, I don't think it makes sense to put the CU key on hold even if it would be possible (I don't know, you need to clarify this with the Limesurvey GmbH), if you solve this issue within the next couple of days. Because from then on you can use the comfort update for any new update that is applying to 3.x LTS or 4.x (which I would currently only install for testing, because I don't feel it is ready for "productive" use yet - we probably have to give it another couple of weeks/months for that).