The italian version of the AD&D Player Handbook explicitly states that you need two separate rolls.
Pag 56 (roughly translated):
To find a trap, the thief must be able to manipulate the item which contains it. Usually the DM rolls the dice secretly...
[...]
Once found, the trap must be disarmed. This roll requires 1d10 round. If he succeed, the trap is neutralized. A failed roll means that the device is too complex for the thief, but he will be allowed to try again once he levels up. If he scores between 96 and 00, he triggers the trap immediately.
Would it make sense to still allow the bonuses of Thieves' tools when trying to disarm it or is there some other item or skill (such as Arcana) that would apply?
Those two cases are not mutually exclusive.
Let's address the skill first, because that's an easy one.
Any character can attempt an Intelligence (Arcana) check to detect or disarm a magic trap, in addition to any other checks noted in the trap's description.
— DMG P 121
So, yes, they can use a different skill.
Would it make sense to still allow the bonuses of Thieves' tools when trying to disarm it
I'm going to address this from two different angles. First as a game rule (i.e. what do the rules, as written, say):
Proficiency with these tools lets you add your proficiency bonus to any ability checks you make to disarm traps or open locks.
— PHB p154
So RAW says "yes".
… but a player who trying to claim a bonus for simply having them would have me calling shenanigans. It doesn't make much obvious sense from a fiction-first perspective.
I'd ask the player to describe how they were using the tools to help them before allowing the bonus. They'd be welcome to invent whatever details they liked, just so long as they justified it.
OK, so, I take a deep breath and spend a moment steadying my nerves. I don't want to have wavering hands for this. I take the copper wire in my pliers and carefully touch one end to the axial manna node and the other to the detection symbol — making sure not to put my hands over the glyph — that should short out the arcana potential and dispel it.
Of course, if they came up with a sufficiently good explanation, I might go past giving them proficiency and skip the die roll entirely:
In most cases, a trap's description is clear enough that you can adjudicate whether a character's actions locate or foil the trap. As with many situations, you shouldn't allow die rolling to override clever play and good planning.
— DMG p121
Best Answer
There's no specific class requirement for the general action of disarming a trap. There's really no specific "disarm a trap" action, either, it's just a thing you can do like other interaction with your environment.
If disarming a trap requires an ability check, the only real guidance is that it may involve a Dexterity check (PHB p. 177).
The main aspects that a Rogue has are:
Under "Detecting and Disabling a Trap" (DMG p. 120):
So, there may be more specific requirements depending on the specific trap. For example, the sample "Poison Needle" trap (DMG p. 123) says that a "DC 15 Dexterity check using thieves' tools disarms the trap", though I'm not completely confident whether that means that having thieves' tools are required in order to even attempt disarming it, or whether that language is just saying that in the Dexterity check one can add one's proficiency bonus if one has proficiency with Thieves' tools. That's just a sample of a kind of trap that a DM might use, though, and each trap can be different. There certainly could be a trap that some DM has used somewhere that could only be disarmed by a character with the knowledge that comes from having the Rogue class. But there are no general requirements that apply to disarming all traps that require any particular class.