The AHHHH! Card spawns the zombie and is then discarded, it is not equipment, it is an event in the equipment deck.
That is how we played it. Otherwise you could use it to soak up a wound later, which makes the card a benefit instead of a negative.
Equipment cannot be used to "soak" wounds. Receiving a wound simply means you can carry 1 less piece of equipment (from 5 to 4).
The only time you can give up equipment rather than take a wound is if your character has the "Is that all you've got?!" ability...which at this point, I do not believe any have.