Essentially, everything works unless it specifically says it doesn't, as per the rule you quoted in the question.
Sneak attack specifically doesn't work in most cases because it requires the use of a particular weapon, however if you transformed into something that could conceivably wield a finesse weapon such as an ape, sneak attack would apply under its normal conditions.
I would agree with all of the deductions in your answer aside from the Swashbuckler's Rakish Audacity and Panache.
My edited list is as follows:
Thief:
- Fast Hands - not likely to work, possibly as Ape at DM's discretion
- Second-Story Work - works as normal, unless the Wild Shape form cannot climb
- Supreme Sneak - works as normal
- Use Magic Device - not likely to work, but situational and at DM's discretion
- Thief's Reflexes - works as normal
Assassin:
- Bonus Proficiencies (disguise kit and poisoner's kit) - highly unlikely
- Assassinate - works as normal
- Infiltration Expertise - irrelevant
- Impostor - irrelevant
- Death Strike - works as normal
Arcane Trickster:
- Spellcasting - not possible in Wild Shape, but spells requiring concentration can continue to be active in Wild Shape if cast before transforming
- Mage Hand Legerdemain - only works if Mage Hand is cast before transformation
- Magical Ambush - does not work
- Versatile Trickster - only works if Mage Hand is cast before transformation
- Spell Thief - works, but would need to come out of Wild Shape to cast the spell
Inquisitive:
- Ear for Deceit - works as normal, unless beast is deaf
- Eye for Detail - works as normal
- Steady Eye - works as normal
- Unerring Eye - works as normal
- Eye for Weakness - works as normal if sneak attack can be triggered
Mastermind:
- Master of Intrigue - no use for disguise kit, forgery kit or gaming set; understanding the languages would remain active but would not be able to communicate in them while transformed
- Master of Tactics - works as normal
- Insightful Manipulator - works as normal
- Misdirection - works as normal
- Soul of Deceit - works as normal
Scout:
- Skirmisher - works as normal
- Survivalist - works as normal
- Superior Mobility - works as normal (except for flying speeds)
- Ambush Master - works as normal
- Sudden Strike - works as normal if Sneak Attack can be triggered
Swashbuckler:
- Fancy Footwork - works as normal
- Rakish Audacity - see below
- Panache - see below
- Elegant Maneuver - works as normal
- Master Duelist - works as normal
My clarifications:
The initiative bonus from Rakish Audacity will always apply, and the
alternative use of Sneak Attack would also apply if the other
conditions of Sneak Attack could be met, namely the Sneak Attack's
specific weapon requirements.
Panache also functions under the condition stated:
The creature must be able to hear you, and the two of you must share a
language.
If you have some means to speak whatever language though magic or
otherwise, the ability will still function.
Obviously some very niche cases where these work, but I just wanted to point out that it is possible.