I want to say Spiritomb which is 1.31% [0.87% [regular] + 0.44[alpha]]) at most during certain times but you get a guaranteed encounter the first time you finish its quest so. After it are some baby Pokemon under 10%. From what I understand, this is rolled only once when the map is loaded with very few locations so its best to not waste opportunity to feed and catch them when you see them. The following are the baby Pokemon whose best spawn rates in an area within a certain time with under 10% spawn rate.
cleffa | 9.82%
munchlax | 3.39%
pichu | 9.73%
magby | 6.75%
happiny | 9.73%
Also again, while these Pokemon's spawn rates are above 5%, they also have few spawn locations which are determined when you load the map. Also Mass Outbreaks are not counted here. Bonsly is 100%, but is only found in shaking ore deposits in Celestica Ruins. Not a baby but similarly, Cherubi and Cherrim is found only in certain shaking trees.
Of course, both Spiritomb and baby Pokemon can be found much more easily in Massive Mass Outbreaks in post-game. It's the non-starter Space-Time Distortion exclusives that cannot be found in MMOs, which while I can't find any percentages, takes 5 to 40 minutes to spawn each time, not even guaranteeing the exclusive Pokemon's appearance. Starters are available in MMOs though.
I am not including any Pokemon who have low rates if they have guaranteed alpha spawns, these are usually fully evolved mons and you can just evolve to get them anyways. Unlike Spiritomb, while they are guaranteed they also respawn. Rare baby Pokemon are more valuable than them because breeding is not in Legends Arceus.
So yeah, Munchlax is the rarest if you don't count Spiritomb's initial encounter. If either Mass Outbreaks or Massive Mass Outbreaks disqualify them both, the Space Time Distortion exclusives might be the rarest if you don't frequent the distortion events. Evolutions of most Hisuian forms are not available in the wild outside of MMOs so maybe them too.
Sources: Various Serebii location pages that includes the percentages and personal experience. Note that some pages may be incomplete because they show in a Pokemon's locations but the same Pokemon won't show in said location's page. Or I might be tired.