The problem is that it's core aspect comes from is it's lore not it's design, in fact if you go back and look at it when it was first revealed a lot of people hated and disliked it and were bashing it for it's design, it wasn't until Mimikyu's lore got reveal that it started gaining more popularity and actually becoming a popular pokemon. So giving it a different form where you would take away it's sheet isn't ruining Mimikyu wouldn't really ruin it's design aspect but instead expand upon it.
You can have core aspects that come from both lore and design. It's not like a Pokémon can only have one, but not the other. The two work together to make the Pokémon what it is. Mimikyu's lore is focused around it dressing as Pikachu to get attention, but its design focuses on the gimmick of the disguise.
I'm not sure why you brought up people's reactions to it though. It doesn't matter what people say about it, it doesn't change Game Freak's original intentions.
Plus it's not the same situation as Unown as they did not choose to look like letters of the alphabet, and it's unclear if people created the Alphabet before they saw the unown or if people seeing the Unown inspired them to make the Alphabet based off the shapes of Unown that they saw. Where as in Mimikyu's case there not born with the sheet in-universe they are born without it and create the disguise themselves, but it's something they choose to do because they want to make friends and they think it will help them if anything it would make sense that Mimikyu would get a form where we get to see it without the sheet.
You're actually reiterating the point I'm trying to make. Unown are Pokémon based off of writing, as that was Game Freak's design intention when creating them, just as Game Freak intended for Mimikyu to be a Pokémon that wears a disguise. Yes, in-universe Mimkyu chose to wear the sheet to garner affection, but that's in-universe justification for Game Freak's choice to make Mimkyu's design gimmick be a Pokémon wearing a disguise.
To further expand upon my Unown example, if we assume writing is based off of Unown, and not the other way around, which is what makes most sense, it's conceivable that there could be some sort of random Unown that didn't inspire a character to write with. The lore doesn't say it can't happen, but it would run counter to the design purpose of Unown, and no one would ever expect it to happen. It's the same with Mimikyu.
I mean if a form changes makes sense for a pokemon then I don't see how it would really ruin the design of said pokemon.
Most Pokémon that change form are designed for it, both lore and design-wise. Mimkyu only has one of those two criteria. Removing Mimikyu's sheet would simply defeat the purpose of having a Pokémon that wears a disguise every moment of its life.
As for having a form that looks like a different pokemon not making sense lore wise, that's not really true, because you could explain by the idea that, that particular Mimikyu grew up in an area where the most popular pokemon in the town wasn't Pikachu, like for instance say one lived Azalea Town in Johto where Slowpokes are pretty popular, if a Mimikyu lived there it would probably create a disguise that looks like a Slowpoke, thinking that it will help it make friends.
Okay, fair enough. That could work. The issue with that is that nearly everything we know about Mimikyu so far suggests that it's an innate psychological trait of the species that causes it envy Pikachu, otherwise it would be hard to believe that universally, every Mimikyu has seen a Pikachu and knows first-hand of the attention and affection it gets.
It's a Pokemon that conceals itself, it has an actual form under that cloth, or did you forget that? Plus it's disguise is 'busted' after being damaged. This form is in no way farfetched or unlikely.
No, I didn't forget that. That's actually the point I'm making. It's very definition is that it is a Pokémon that conceals itself. Taking away its disguise would be taking away it's defining characteristic.
Is there any official material stating that the negative effects of seeing its true form are caused by it being hideous? Most of the references make it sound more like its some kind of magical power or curse that its body exudes if someone sees it. In-game a Mimikyu even references it being able to curse people, as does the Mimikyu in Mimikyu's song.
The Pokédex descriptions suggest as much, as does the anime and initial reveal information on Mimikyu.