As excited as I am about trying out BW, my players are of the more casual variety. Maybe a few of them would enjoy it, but not the whole group. 
Sad panda.
Never know 'till you try, right? I say, grab the four “most promising” ones, run The Sword, see what they think.
If they don’t like it, bummer, but you’re no worse off. If they do like it, maybe they’ll help you convince any holdouts.
Players worrying about “lot of funny looking boxes and cryptic stuff” sounds like a bad sign on the surface, but they’re not worried about the system, they’re worried about their own ignorance. Show 'em that those boxes actually do make sense, and the problem’s gone! (He says, making it sound like a much simpler problem than it is… but still, can’t hurt to give it a shot, eh?)
Or maybe you can trick them by copying character info onto smaller sheets of paper in simple categories. So they start out with, I dunno, just the Beliefs, Instincts and Traits on one half-sheet page. Then when they want to do a skill, hand them their Skills sheet, or if they want to do a stat test, hand them the Stats sheet - and that could be a separate sheet from Attributes. And have it be just the numbers, not the little boxes and all for keeping track of tests. Maybe don’t even put shade. When combat happens, hand out a sheet with just the PTGS and some really, really simple weapon stats. When they need equipment, hand them an equipment list (with Circles and Resources tacked innocuously on at the bottom, perhaps? Or Reputations and Affiliations? Or maybe keeping it as simple as possible is best.)
Then, when they complain about the sheaf of (utterly clear but inconveniently numerous) papers they’ve found themselves holding on to, introduce the (much simpler in comparison) REAL character sheets, after they’ve already accepted the individual components. It’s like Gandalf introducing the dwarves to Beorn!
Disclaimer: I have never actually tried this. It may or may not turn into an utter disaster. Though I suspect at worst it would be a memorable disaster, amusing in hindsight. One can do worse at the gaming table.
I will try 
We’ve just got a very busy group who don’t like to spend time learning new complex games that don’t have immediate payoff (like a boardgame). Add a baby, a player who travels, and a non-native English speaker who gets overwhelmed and…well…you get the idea.
To be honest, most of the BW character sheet is rules reference (not usually found on RPG character sheets).
You could cut it down to BITs, skills, and attributes, and be just fine, I think. Don’t even bother marking out advancement, if you’re gonna run The Sword. If I had more time on my hands, I’d hash it out.
The easiest way to figure out whether or not your group would enjoy a Burning Wheel campaign is to share with them the Hub and Spokes and see if they get anyone interested, and spend a session playing through The Sword so people get an idea of what the game is like before undertaking your own.
Voila! 
Thanks, Andy. With all the people offering help, I’ve been trying to stay on the periphery of this discussion.