I want to solve the "Missing in Action"-quest non-violently. It's said that I need an Legionaire Imperial armor set, my selfcrafted Imperial one failed. But where to get the items?
You can't. The linked answer is incorrect; such armor does not exist.
It's actually not possible to complete this quest peacefully. There is an Imperial Decree that is not available without the use of the console that appears to be the key to this quest, but it was apparently excluded from the game as the result of a bug or some other unknown reason. Not only is it not present in the actual game, but the console-obtained version doesn't do anything.
Source: UESP Quest Page
The strategy guide says that there are 3 options.
Edited. UESP has conflicting information, attempted and failed. The option isn't available, but should be. Some programming error or something keeps it from working right. So, no not until it's patched or fixed either by Bethesda or modders. No peaceful solution exists, and there is no such armor. A book related to the quest can be gained using console commands, but it does nothing aside from take up inventory space.
You can't obtain the Imperial Legoinaire Armor as it doesn't exist. But however, there is another way to release Thorald without bloodshed.
Release Without Bloodshed, Step 1
What you'll need to do is join the Imperial legion and you need to start the rescue quest. Talk to General Tullius in the Castle Dour in Solitude to release the prisoner at Northwatch Keep. He will give you the Imperial Orders you need to give to the Thalmor at the front gate. This will cause the Thalmor at Northwatch Keep to become unhostile.
Release Without Bloodshed, Step 2
Now, go to Northwatch Keep. Talk to the Thalmor at the front gate and persuade him to release Thorald Grey-Mane and give him the Imperial Orders. He'll lead you inside the keep and you need to talk to Thorald to tell him he'll be rescued. then he'll follow you all the way outside. Don't worry, as the Thalmor will still become unhostile for the rest of the gameplay.
Release Without Bloodshed, Step 3
Now you released Thorald without having to kill the Thalmor. Talk to Fraila to complete the "Missing in Action" quest.
You can't obtain the Legionaire Armor to relase him, but you do want to do what is above. That's how you do it. The Wiki says:
But if you have the Unofficial Patch,
Then you can release Thorald without bloodshed and but no Legionnaire Armor!