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 Most of the points that make your character who he is are almost entirely role-playing choices rather than mechanical rules choices. The "fluff" (flavor) and the "crunch" (rules) are two completely different things, and backing up a narrative choice with a mechanical element like a power or a feat is simply a choice rather than a necessity.

 One of my characters is a 1.5-ft-tall shapeshifting fey crow spirit named Jack Daw. (Who, coincidentally, also happens to have a nasty habit of snacking on recently deceased opponents.) He fights shaped as a crow, wheeling and diving at opponents to confuse and distract them before slashing them to ribbons with his claws. He's loud, rude, raucous, insatiably curious and greedy. Born in the Feywild, he ended up in this world after seeing the Raven Queen flying through the Feywild in the shape of a crow, fell completely in lust with her, and chased after her trying to get laid.

Does any of that sound like either a pixie or a druid? Even being 1.5 feet tall, Jack is still one-and-a-half-times the size of a regular pixie according to the pixie's racial write-up.

"Shapeshifting fey crow spirit" is not a race or class available in the 4E D&D rules, but a pixie druid certainly is, and does pretty much all the things I wanted my character to do mechanically. Pixies can fly, and druids can shapeshift into creatures of their own size (but don't gain any extra abilities from it, such as flying). A pixie druid, therefore, can turn into a crow and fly around. Charging in combat is a well-supported tactic with a lot of items, powers and feats to enhance it, and druids can be built as very effective chargers - many of their beast-form powers are meant to be used when charging and there are several druid-only feats that provides benefits on a charge. A flying pixie can charge vertically as well as horizontally, and they also have a feat that benefits charging.
 Jack follows all the mechanical rules of being a pixe and a druid, but according to the in-game narrative, he's neither. As long as I continue to follow the rules of the mechanical choices I've made for my character, I can flavor it however the hell I want (subject to the DM's approval, of course).

 Now, pertaining to your "beastman" character...

  Since you're going for a more "civilized" beastman archetype, you don't really need to take a lot of mechanical choices that play up your bestial nature. I'd personally just pick either Goliath or Longtooth Shifter for your race and leave the rest of it up to your in-game fluff and roleplaying choices.
Goliaths, for example, are supposed to be about eight feet tall, but are still considered a Medium race. The "Medium" size description is simply a shorthand for the mechanical expression of the size-related rules that Goliaths follow - every Medium creature, from a 4-foot-tall dwarf to a 6-ft-tall human to an 8-ft-tall goliath occupies a 5ft x 5ft x 5ft square according to the mechanical rules of the game.
 You could, if you wanted, play a goliath and simply have most of the fur/fangs/claws stuff be pure fluff. Their ability score bonuses and racial power are suited to a large, powerful creature, and are excellent for a fighter. They also get a bonus to their Nature skill, which could be refluffed as the character's bestial nature.

 Shifters are essentially the "beastman" race in the game, and the longtooth shifter race's ability score bonuses of Strength and Wisdom line up perfectly with the fighter class. They have bonuses to Athletics and Endurance, which line up with a beastman character. They're not necessarily exceptionally large by the height/weight notations in their racial write-up, but it's fairly  easy to imagine that they could be the same size as the goliath.

So, either race works.

 As a fighter who wants to use big weapons, neither taking the werewolf theme nor multiclassing druid to pick up wild shape to gain a beast form will do you much good - you can't use weapon powers that lack the beastform keyword while in beastform.
 If you want to wield two one-handed weapons rather than a single two-handed weapon, you could take the ranger multiclass feat Two Blade Warrior and get free training in one ranger skill (Nature, Survival or Perception would be best) as well as the ability to wield one-handed weapons as if they were offhand weapons. Then you could take a superior weapon proficiency feat to get either a bastard sword or waraxe.
Note, however, that holding two weapons won't allow you to attack with both at once unless you take fighter or ranger powers that allow you to do so.