If it ain't broke, don't fix it.
I think your rewrite of the psychic blades ability makes it significantly stronger, and your reasoning doesn't add up.
#1: Prevalence of Resistances
You are correct to observe that resistance to psychic damage is much more rare than resistance to slashing, piercing, bludgeoning, unless we break the latter into its two categories. Resistance to all slashing, piercing, and bludgeoning is far more rare than resistance to non-magical slashing, piercing, and bludgeoning. The moment your rogue gets access to a +1 magical weapon, this particular argument of yours no longer applies.
#2: Ease of Use
You are correct to observe that psychic blades is easier to use, but this is only the case when you have remaining bardic inspiration. The reasoning you give here is already baked into tying psychic blades to a limited resource. A 20 charisma 5th level Bard (which is very generous) can use up to five bardic inspiration per short rest. It's easily conceivable for a rogue to use sneak attack every or nearly every turn of every combat without expending any resources at all. You bonus-action-hid last turn? Sneak attack. Your paladin is in melee with your target? Sneak attack. For free.
And you must further consider the opportunity cost of psychic blades. You burned your inspiration on psychic blades? That means no bardic inspiration for any of your allies to get those precious extra points to beat that tough DC.
#3: Your proposed solution
You propose, "to use the Psychic Blade feature, you don't need to spend a Bardic Inspiration, you need..."
(1) Advantage on a charisma check
You clarified this in comments saying "I mean that you can use it if something gives you an advantage on checks that involve charisma and that target the thing you want to target (e.g. friends give you advantage on charisma check against a target)".
So I burn an action at the start of the fight to cast friends. At the cost of a single action, I get to use psychic blades every turn until my target dies. This is part 1 of "make psychic blades more easy to use".
Additionally, there exist magic items that just give permanent advantage on a type of charisma check, such as Far Gear (Acquisitions Incorporated, pg. 221). Being attuned to an item such as this would mean permanent psychic blades at no cost whatsoever.
(2) Under Mantle of Whispers
The setup for this is pretty tedious, but it actually works against you. Mantle of Whispers remains "until you use it or finish a long rest". As long as you don't use the ability's primary feature, you just got psychic blades for free every turn, even more available than the rogue's sneak attack, without expending any more resources.
Unless you meant "you have used the shadow and are now in the disguise". This needs to be clarified. Still lasts an hour. Still get psychic blades for free for a whole hour. This is part 2 of "make psychic blades more easy to use".
(3) Target is charmed or frightened
Now you're just adding more conditions to make psychic blades go off more than it ever did as originally written. This is part 3 of "make psychic blades more easy to use".
A Whispers bard with this rewrite is almost certainly going to use psychic blades more than he ever did when it was tied to his uses of bardic inspiration.
Conclusion: Your house rule takes a non-existent problem, and makes it into a very real problem by doing the exact opposite of what you intended.