There are two questions I ask myself when approaching this kind of problem.
In what other ways can this advantage be emulated?
If there are any, then these other ways can be referenced to get a basic idea of what advantages you are really granting. If there are no other ways, then you are in unexplored territory and you have to be extra careful.
How well can this character leverage the advantage?
This relies more on your understanding of the character in question, and sometimes of the player as well.
These questions are open eneded because there is no "one size fits all" assessment to determine if something is balanced. Answering these questions meaningfully requires some degree of system mastery, and often involves scanning through the relevant material. Fortunately, 2e.aonprd.com's searchbar makes it relatively easy to find the relevant bits. Either way, assessing balance is difficult on the fly, so when you give out rewards you can say something like "I'll figure out the specifics later".
I can look at your two examples to show you how I would answer those questions.
Using a two-handed weapon with one hand cannot be achieved in other ways.
From here, I would start by comparing a two handed shotgun to a one handed shotgun. Moreover, both shotguns still require two hands to reload, though there are solutions for similar quandaries, such as the Capacity trait or the Dual-Weapon Reload feat.
Overall, the advantage you gave the gunslinger is equivalent to a one-handed shotgun with increased die size, firing range, and scatter range, while also granting her a Dual-Weapon Reload feat that only requires that shotgun. That is a lot to give out, not even a Inventor with Weapon Innovation would be able to improve a shotgun that much.
That said, let's consider emulation from a completely different direction. Both the Core Rulebook and Grand Bazaar have sections written with disabled characters in mind. The relevant bits are a bit scattered, but basically:
A character with a missing hand or arm might need to spend 2 actions to Interact with an item that requires two hands, or otherwise compensate. Using a two-handed weapon is not possible. A character can acquire a prosthetic hand or arm to compensate.
A prosthesis is an artificial device designed to replace a missing or damaged body part. Prostheses are made from a variety of materials, including wood or metal for common prostheses and clockwork devices or rare materials for more expensive ones. Advancements in the prosthetic field mean that even the most basic of prostheses can provide the full range of functionality for a missing body part.
A one-armed character can acquire a prosthetic that completely makes up for the missing arm. Only allowing a the Gunslinger to use a two-handed shotgun instead is less powerful than granting her said prosthetic, and therefore unbalanced.
Even so, ruling in the moment that the one-armed Gunslinger could use her weapon of choice to cut the dead fish was the right call, because:
By default, we recommend that, in an unexpected situation, you rule to allow the character with disabilities to participate fully in the story.
The problems start if the Gunslinger gets a new arm or prosthetic while retaining her ability to use a two-handed shotgun one-handed, then she will be able to leverage this advantage: all the benefits of a two-handed weapon build (better damage, traits, etc.), while behaving like a different kind of build. She could keep her hand free to use other items and skill actions, wear a shield, even dualwield two two-handed shotguns...
This isn't something I would personally give out as a reward, at least not without some serious detriment. It's possible that when you say "trained in using the shotgun one-handed" you implied a detriment, because the gunslinger is otherwise expert or better with firearms. An effective -2 penalty might work as a detriment, if the player doesn't find a way to circumvent it.
The Bard could gain the Martial Performance feat via the Multifarious Muse feat. That first level feat would grant him proficiency in all Martial Weapons (including a Cane Pistol), which in the Bard's case means trained from level 1 and expert from level 11. Finding a Cane Pistol in the first place is matter of setting and access, not balance.
However, giving the Bard expertise in a weapon before level 11 is a big no-no. The differing rates at which martials and casters acquire proficiencies is a cornerstone of the PF2e's balance. The only published exception is the Sixth Pillar archetype which has been flagged for errata for that very reason.
There isn't much for the Bard to leverage given that the advantage in question is less broad than a level 1 class feat. While the Cane Pistol is interesting, it's balanced compared to other martial weapons, a handful of which every Bard is proficient in by default.