Can I use the Injury and Madness cards from Miskatonic Horror without Dunwich Horror?
It's possible to houserule anything, and these cards aren't an exception.
Just have in mind that if you want to add these in using just the Dunwich Horror rules, it will decrease the game's difficulty considerably.

In the core game when your Sanity or Stamina drops to 0 you:


Discard half of your items
Discard half of your Clues
Recover 1 Sanity or Stamina


The Dunwich Horror leaves the above possibility intact, but also gives you an option to instead:


Keep your items
Keep your Clues
Recover full Sanity or Stamina
Gain an Injury or Madness card


Like this, it's already a convenience.
As it's entirely a player's choice to gain the Injury/Madness card, you'll simply choose the option that's less harmful in a given situation.
While Injury and Madness cards are somewhat debilitating, in many cases it's still more desirable to gain one than to lose your clues, stuff, and time needed to heal yourself.
To balance this, there's a risk included: If you ever gain another copy of the Injury or Madness you already have, you are instantly devoured.
If you only have Miskatonic Horror, you never risk gaining a second copy.
With this mitigating factor gone, Injuries and Madnessess become a more attractive option.

If you're fine with an easier game, then you're done.
If not, you have a lot of options in front of you. We're talking about house rules after all.


The easiest modification would be to remove the base game option of losing half of your possessions.
When gaining Injury/Madness is no longer a player's choice, they will more likely hit you when it hurts.
You may also consider a "baseball" variant:
When you have three "strikes" (total of both Injuries and Madnesses) you are instantly devoured.
This would be a proxy of the "double copy = devoured" rule.


It's impossible to list all the potential variants. I'm sure you'll find something that suits your gaming group.