A barrel extension wrench is for removing and installing barrel extensions.
Tweaking front sights into alignment is usually going to require very little movement.
Sometimes, simply loosening the barrel nut and holding the sight the direction you need to move it while re-torqueing the barrel nut will fix it.
Make sure to grease the front of the barrel extension flange so the barrel nut torques against the grease and it will not force the barrel to move as you torque the nut.

Very few people putting together AR-15's have a legitimate need for a barrel extension wrench.
As I specialize in BUILDING AR barrels, I obviously use one every week, but there is no need to remove extensions otherwise.
During the process of building a barrel, the extension gets torqued into place and then the pin is installed.
The gas port is drilled at TDC as determined by the indexing pin.
Moving/swapping the extension is almost always going to change the reference and the gas port/FSB is not going to be TDC anymore.

For you non-mechanic types, TDC=Top Dead Center, a term used when working arond engines, usually the crankshaft position where cylinder #1 is at the exact top if it's travel in the compression stroke. In the case of barrels, you can think if it as 12:00.

Quoted: FWIW, I have never seen a barrel extension "wrench", although like the sockets designed and used primarily by Armalite; I have seen barrel extension sockets (which fit into the chamber end of the barrel extension locking into the actual lugs, like the bolt and are used in conjunction with a barrel wrench to tighten the barrel nut when installing a new barrel) for both the AR15/M16s and the AR10s. Mike ps - sorry cannot say when or where as these items are rarely seen outside of the company listed above, which if my info was correct, were the first to machine and use such a device for mounting and un-mounting barrels........, I can tell ya they are slick little devices and make assembly and dis-assembly much easier.

Potatoe Potato...

Brownells Link also lists them as a "wrench", even if they are more like a socket.

Quoted: WOW, was not aware you could actually buy one of those Randall, as at the time I saw the ones I have seen and used they were "handmade" by a machinist friend, who told me that Armalite held the patent on them.....

I hand made my first ones too.
Now they are easily available and the ones from Brownells are very well made.
I have both of them now.