In terms of strict canon, for whomever cares, the lowest registry number on a strip-phaser ship indeed belongs to an Ambassador - USS Zhukov, NCC-26136. That is, this is the lowest-registried Ambassador that was actually seen on screen; backstage sources give lower registries for two other ships, including the class ship.
The second-lowest-registried ship type that is known to have strip phasers would be Niagara, a similarly sized vessel that has Galaxy style nacelles. The lowest noncanon example would be USS Wellington at NCC-28473, but we never actually saw that ship on screen and we could speculate that it had an earlier type of engine and perhaps lacked strip phasers and whatnot. When we do see a Niagara, she carries a much higher registry (USS Princeton is NCC-59804), perhaps indicating a later production batch and possibly suggesting more modern systems than on the Wellington (although one would think that the earlier ship was also refitted at some point).
Of course, we can speculate that the early Ambassadors also lacked strips and were refitted with them only later on, prior to the 2340s when the E-C was lost. So we can't be completely sure about the date of the introduction of strip phasers. But I do like the idea that they originally only existed on the largest ships, these being the two-engined Ambassador and the three-engined Niagara from the very early 24th century. They'd only be introduced to medium starships at around the 2340s-50s timeframe and the NCC-50000 registry range.
Timo Saloniemi