Two different answers for two different editions
Traps in HQ, with the odd special exception in some Quests notes can be set off by stepping on a particular square, opening a chest or a door
Under SERules of Play p13 wrote:If a player searches for traps in a room that contains a trapped treasure chest the trap is found and rendered harmless
As, under SE, opening chests is handled in the same way as opening doors, I would assume, although it isn't stated, that door traps are handled the same way as chest traps.
And traps on squares are also rendered harmless or automatically set off when found (depending on the trap type) so in SE the disarm mechanism never actually applies to traps that haven't already been set off (which does raise the question as to why it is called "disarm")
Under NA (which I assume is the edition that the OP is discussing)
"As a Hero you can only search for traps if there are no monster visible to you", no mention of Line of Sight so I don't agree with that part of the OPs statement (although it has no bearing on the disarm question)
Having search for traps, Zargon points out the suspect squares, or the suspect chest (and again you would assume that he also points out suspect doors but this isn't stated). Once you have discovered the suspect squares/chest/doors the rules refer you to the Disarm section on page 21
This section of the rules states that to disarm a trap you must move onto the trapped square, which is fine for traps located on a square but there is no reference to how you disarm chest or door traps. You cannot move on the trapped sqaure in the case of chest traps as the square has a chest onto and you can't move onto furniture, and in the case of door traps you cannot move onto the door square as doors are located in walls that sit between squares, so a gap in the rules.
As an SE player personally I would assume that, as you need to move adjacent to a chest or door to open it, then you would have to do the same to disarm them, but under NA rules, whilst you DO have to move adjacent to a door to open it and therefore the assumption that you have to be adjacent to a trapped door to disarm it seems reasonable*, strangely you don't have to move adjacent to a chest to open it under NA edition rules, in fact you don't have to open a chest at all. The contents are just 'recovered' when you search the room containing the chest for treasure.
*Although if chest traps are automatically disarmed when found then why not door traps?
p18 does state "A treasure chest or piece of furniture may also contain a trap. If you search for treasure without first searching for traps, you will spring the trap" which could be taken to mean that searching for traps in a room that contains a chest trap automatically disarms it, so the question of where you place your figure to disarm it never arises.
To be fair the whole handling of search and disarm in both editions is poor and I don't agree that it is a necessary evil, just an evil, see this thread for more suggestions on reworking this flawed aspect of the game
Search – The Binding Topic