Even using magic to restrain a person so that you can lop off his head is also a violation.
This is false. (By which I mean: I believe this is false, and am attempting to make the point that stating opinions as facts is not particularly useful. Please note that the rest of this post is my opinion, and you should go with whatever definition of the first law works for your gaming group.)
Why? Basically, it totally hamstrings the wardens. What can they do to make an arrest? Well, they can't use magic, because if it directly leads to the arrest, well, the death of the warlock is a direct consequence that can be expected after that, even if there's an intermediate "trial" and the actual execution is done by someone else. Just directly contributing to death can't be enough; that'd give out lawbreakers to, for example, anyone who uses magic to attack someone that's killed during combat, regardless of the source of the death blow.
The dividing line I use is whether or not there's any additional act of free will involved.
So, if there's a fey there that's sworn to kill the guy, and you restrain him, that's a first law violation - the fey killing him once restrained isn't an act of free will, and thus the death is metaphysically directly caused by your spell.
On the other hand, if you restrain a guy, fully intending to personally slit his throat once that's done - that's not a first law violation - it's "merely" murder. Why? Because the actual death wasn't caused by magic; it was a separate act of free will. The GM would, of course, be perfectly justified to have various mundane complications come up from doing that, up to and including the wardens investigating you, but it's not justification for a lawbreaker power.
I'd also say that, if you kill a human using the weapon:6 power of a warden sword, that's a lawbreaker - see all the normal rules for responsibility for use of enchanted items. But if you're using it as just its base weapon:3 really sharp sword, no lawbreaker; that's killing someone with a sharpened hunk of metal, no magic involved.