What you're essentially looking for is a list of TMs/tutors from gens 3-4 that were discontinued as such in later games, so for most Pokemon the only way to get a hold of those moves is from those early games, in which hidden abilities didn't exist.
Sword/Shield brought back several old moves into the TM/TR rotation, leaving only two Gen 4 TMs that aren't replicated as TM/TR/tutor in any subsequent game: Silver Wind and Natural Gift. As such, apart from the limited selection of Pokemon that can learn those moves by level-up or egg, most Pokemon can't have that move coexist with their HA.
Tutors are another possible source. There were some gen 3 tutors whose effect was to replicate certain RBY TMs. Four of those--Double-Edge, Counter, Mimic, and Soft-Boiled--are again nonexistent as TMs/TRs/tutors in any later game, but once transfer support was added between the VC games and Pokemon Bank, it became possible for some Pokemon to get the moves from there instead and have guaranteed HA from transferring forward. Still, some Pokemon had the disadvantage of not existing in RBY so they couldn't get the moves from there, or of not being compatible with them back when they did exist as TMs. This was the case for Softboiled--originally, as a TM, it was very limited in its compatibility and allowed only Chansey and Mew to learn it. The tutor version was still selective but now slightly more forgiving, extending compatibility to the Cleffa and Togepi lines. Those species can only get the move by this method, which of course means no HA either.
Gen 4 tutors that haven't been used since are more numerous: Air Cutter, Fury Cutter, Ominous Wind, Sucker Punch, Vacuum Wave, Ancient Power, Mud-Slap, Rollout, and Twister. Most of those moves aren't very good, but Sucker Punch is often used on Pokemon that can learn it this way and no other.
As another possibility, there were some obscure GameCube games that had compatibility with the GBA games, which allowed access to unique moves like a Moltres with Morning Sun, as well as several events in that era (Chansey with Wish, Entei with Extreme Speed). No HAs on those either.
Note that in a couple weeks, the Crown Tundra will be released, and one of the features that's been publicly acknowledged to come out there is an item called the Ability Patch. While the Ability Capsule can be used to switch back and forth between one non-hidden ability and the other (only for species that have two distinct possibilities), this is a different item that can change any Pokemon that has a potential hidden ability as a species, to actually have that ability (but it's a one-way trip, so no changing from HA->normal ability). After that point, the only thing that can possibly make a certain Pokemon incompatible with its HA is if the species as a whole still can't be transferred to Sw/Sh at all even after the second Pokedex expansion that's slated for that release.
