If you are using a script that is similar to the script "doorkey.fpi" that the Door (key) would use, then all you have to do is modify the script so it will not return to the state that displays the hud when you "unlock and open" the door.
For example, if you look at the doorkey.fpi script, you will notice this line:
:state=3:decframe=0
:state=3,frameatstart=0:state=10,setframe=0
This state will close the door and then returns the script back to state 10, which will display the hud when the player is within a distance of 60 units. In your case, I would alter the state=3 line to something like this:
:state=3:decframe=0
:state=3,frameatstart=0:state=20,setframe=0
Since the door has been unlocked, I can pass through it and once through the door closes after I am 60 units away (state=2 line). As the door closes (state=3), the script will go to a state=20 line, which there is nothing left to process and therefore the script ends. The hud will not reappear when you pass the door, and remember that since the script ends you will not be able to open the door again.
There are other alternatives, but this is the simplest method.

Twitter: @NFoxMedia