In 2e, traps are there specifically to slow down the party and force them to be cautious. Even in 5e, traps are a break in the action and can be triggered before anyone sees them. The 2e style doesn't sound like your playstyle at all, but even the way 5e uses traps by default seems to not be your style either. So...
Tell them the trap is there
Traps are interesting when players interact with them. Tell them the trap is there! Yes, 5e has Passive Perception for this purpose, but don't let that ruin your fun if giving the check away "for free" will significantly improve your and your players' enjoyment of the game. (Passive Perception is still useful for surprise encounters and ambushes, after all.)
By telling them that a trap is present without telling them exactly where and what, you get straight to the interesting interaction, as they investigate the trap to figure out where it is, what it does, and how to circumvent or disable it. They may play it smart or they may make mistakes and suffer the trap's consequences. Some traps will be boring (and quickly dispatched) and some will be super-interesting (and be super-interesting). Either way—smart or disastrous, trivial or super-interesting—you are keeping the part of traps you find fun (the players messing around with them), eliminating the part you find frustrating (caution bringing the dungeoncrawl to a literal crawl), and quickly moving along to wherever the fun is actually to be found.
So skip straight to the fun, and tell them that there is a trap here. Let them figure out what kind and where exactly, but tell them:
As you move to cross the threshold, your keen adventurer's survival instinct tells you something is wrong. There's something not quite right about either the door's stone frame, or the room's floor… or maybe it's something else nearby that's off. Anyway, what do you do?
...and cue the flurry of investigation!
DCs for the traps, should then be converted like most DCs in 5e. 10 for easy, 15 for moderate, 20 for hard, 25 for very hard.
There are two ways to interpret that sentence, and it hinges on a weirdness of how English uses the indefinite article.
Any character or monster that doesn’t notice a threat is surprised at the start of the counter.
The usual interpretation of "a threat" here is that it means "one threat". If that is the correct reading, your question is the result. Is it correct though? This meaning would require that surprise is a relationship between two individuals, so that the dire wolf could be surprised by the rogue but also not surprised by the enchanter.
Is this how surprise works? It turns out, no:
If you're surprised, you can't move or take an action on your first turn of the combat, and you can't take a reaction until that turn ends. (PBRv0.2, p. 69)
Surprise is not a relationship between two entities, it is a state of a single entity. It's impossible to be surprised by one opponent but not surprised by another.
Is there another way to read that sentence about "a threat" that makes surprise sensible as a state? As it turns out, yes.
"English is funny that way"
Another use for the indefinite article, which looks identical to the "one threat" meaning, makes the sentence in question
Any character or monster that doesn’t notice a threat is surprised at the start of the counter.
mean any threat at all, not just one. If this meaning of "a threat" is how it's being used, then that means only creatures who notice no threat are surprised.
Because this reading is perfectly normal English, but ambiguous, we need to confirm the reason by looking for clues in the surrounding text. That confirmation is in the definition of surprise we looked at above: being surprised means being completely surprised, which only makes sense if it happens when no threat is noticed.
So the dire wolf is not surprised, because it did notice a threat, as opposed to not noticing a threat. (See how that makes sense put that way?)
On the plus side, the champion and the rogue don't need surprise to have advantage on the dire wolf, because that doesn't rely on surprise, but rather on being unseen, and being unseen is a directional relationship, not a state.
Best Answer
Strictly speaking, you typically use either Wisdom (Perception) or Intelligence (Investigation) to locate the trap, then a Dexterity check (with thieves' tools) to disable the trap.
Asking the player for a further Investigation check to understand a trap that they've already seen is a valid use of the skill, but it's not typical. Normally you simply use Perception to spot it, then Dexterity to disable it.
In the event that the DM asks the player for a Investigation check to understand the trap before attempting to disarm it (something which would be more likely to apply to especially complex traps), it's entirely up to the DM what happens.
From the Player's Handbook:
Perception:
However, Investigation can also cover the skill of finding a trap: