You've got some good responses already, but I wanna clarify what "speshul" actually means.

The thing is, you can have any kind of character whatsoever and make it not speshul, it just depends on how you write it. Let's take the ever-popular Sue trait of beauty.

Beauty + speshulness gives you a character whose beauty causes others to instantly love them, regardless of any other circumstances that would normally lead them to react otherwise, such as the fact that she's written as a spoiled teenager, or perhaps she's just wandered into someplace she has no business being and started demanding attention. But that's okay, because her surreal loveliness means others can instantly tell she's a good person! Speshul beauty means all the men want her, all the women want to be her, and anyone who doesn't love her is obviously evil. Mr. Right will always fall for her eventually, and they'll live happily ever after because she's just so pretty.

Beauty - speshulness is entirely possible, though. In this case, her looks won't save her from getting into trouble if she waltzes into the Council of Elrond and insists on being sent with the Fellowship, which hasn't even been decided on yet. If she's human, all the elves are prettier than she is, and they don't care—she's in trouble, period. If she acts like a spoiled teenager, other people will treat her like a spoiled teenager. If she actually is a good person, she'll need to learn to act like one before people will treat her like one. If all the men want her, that might be pretty annoying or even dangerous when it turns out some of them are bad people, and she's going to have to contend with the fact that they only want her for superficial reasons. (Some speshul characters angst about this, too, but don't be misled—it has no impact on them as people, they won't learn anything from it, and it's only in the story in a shallow attempt force the audience to feel sympathy for them.)

Or maybe she's okay with that—maybe she's a man-eating megab*tch and loves it, and the audience is allowed to dislike her for it rather than having the narrative insist that this is right and good behavior and anyone who doesn't like it (and her) is an idiot.

In a nutshell, speshulness is all about whether the people and the environment around the character react appropriately to them, regardless of whatever traits they possess, and whether the traits are there to advance the story and make the character grow rather than to make the character more awesome. Speshulness means the character doesn't have to work for her achievements; they're inevitable.

So, if you're picking character traits just because they're cool, or they let your character do cool stuff, you're going to want to step back and re-think that. Instead, pick character traits because you want to tell a story about them—pick traits that will give your character something to overcome. Character growth makes awesome characters. Giving them cool abilities/traits to make their life easier to start with makes them boring, and yes, maybe speshul.

~Neshomeh

It's best to limit the agents to what inhabitants of the canon they're in could/would do. The Magician agent can definitely do missions in Middle-earth. Could s/he use a bit of magic in an empty cave in Moria, where no one would observe the spell or its effects? Certainly! Could s/he use a spell to assassinate a Sue if no canons are around to see? maybe, as long as the Magician and his partner dispose of the body so no canons come across it, and the signs of being killed by an uncanonical spell. Could the Magician use spells in the middle of the Prancing Pony in the broad light of day? Hell, no. (Unless it was accidental bad luck screwing over the agents, but in that case, they'd better whip out the neuralyzer pretty damn fast.)

(I'm assuming that by Magician you mean some kind of magic-user, and not an entertainer who performs at children's birthday parties. Although that would be pretty fun, too.)

Plus, don't forget! This Magician will probably be disguised as something different in Middle-earth. So he'll have the appearance of a native helping him to stay off the radar.

I'm not the world expert on LotR myself, but I am aware that there are magic users (Gandalf, for example) that exist in Middle-earth. If your agent is or is disguised as a canonical magic user, I don't see the problem with using one.

If you plan on using, say, a protoss High Templar that will psi storm the living daylights out of an area and hack foes to bits with psi blades well... not so much.

For example, one of my agents is an elemental mage, but she really only tends to use her magical abilities in places where it's not uncanon for magic users to be or in HQ. It's personal choice, at the end, but I think as long as the agent's not a Maia or other equally uber-powerful magic user, you should be all right.

Also, you'd have to think about how well the use of magic fits in with the mission you're writing. Is it necessary for magic to be used, or can they get by with using more mundane methods to gank the Sue?