Yes, the 23.35 mm (nominal size*) extractor is a must for working on old** SL cranks, Don't install one of those cranks without having the correct extractor in hand.

* note, threads always measure smaller than their nominal size, because the peaks of the threads are truncated. So a nominal 23.35 mm extractor might measure 23.0 mm with calipers. A nominal 23.0 extractor measures something less than 23mm. Yes it's a terrible situation for users and mechanics. You have to know what size your extractor tool was made for.

Having a 23.0 mm extractor (made for TA cranks) is the worst thing possible, because it'll fool you into thinking it'll work, then it'll strip the threads from the crank. Sometimes it even works, if the crank wasn't installed tightly.

Trying it with a much more common 22.0 mm extractor (Campy size) is safe, since there's no mistaking the fact that it's way too small. It's the TA tool (or Park equivalent, for example) that has killed so many SL cranks.

**At some point (early'80s?) SL switched to 22 mm extractor threads. So it's just the old ones that need the "proprietary" 23.35 mm tool. Luckily there's little confusion between those two sizes.