Yes, it requires an action, but...

Ignoring the Charm effect, as you mentioned, the wolf, regardless of intelligence, is still subject to the rules of the Animal Companion feature. That means that the wolf still requires an action to order it to attack and I would impose that. (Beastmaster ranger is, in my opinion, weaker than Hunter ranger, so you might want to weigh out how much damage it would actually be adding, but RAW, yes it would still require an action.)

However, I would argue that, so long as your Ranger already has the Extra Attack feature, the wolf can act on its on, on the Ranger's turn as it previously did--the only difference being that your Ranger no longer has to verbally command it (personally I find that a fair trade-off for 1000 GP, but mechanically that is your decision).

However, remind the players that they need to take caution with how they treat their awakened wolf friend--according to the text of the Awaken spell, you could still impose the ability of the wolf to leave the party if you so chose. However, since you mentioned ignoring the Charm effect due to Animal Companion, I don't know how that would work out; it might be more of a plot device than anything.

TL;DR, I think your players have a legitimate argument, but I would keep the rules of the combat the same so you don't have to roll extra initiative counts or anything (WoTC always likes to point out that rolling more dice is usually bad, because it makes a combat slower). You could however, add the bonus that the Wolf doesn't need to be verbally commanded (it still uses one of the ranger's attacks, and attacks on his turn though).

You get one attack

You are not taking the Attack action so you don't get two attacks from Extra Attack (emphasis mine):

you can attack twice, instead of once, whenever you take the Attack action on your turn.

Instead, this feature gives you a separate benefit: "make one weapon attack" when you command your beast to Attack:

You can use your action to verbally command it to take the Attack... action