Well, were I you, and I'll likely be doing this even though I'm not, here is how I would work a homebrew conversions:
1.) Figure out which IH classes are redundant to 4E core classes - eliminate them.
2.) Figure out which 4E core classes are redundant or a violation of IH themes - eliminate them.
3.) Look at the pile of eliminateds and see which might work cause you want them to work - put them into a maybe pile.
4.) Decide yea or nay on the various IH sub systems you want to import into 4E. Of those divide them into meld or pure imports.
5.) Begin working out the sniggly details of making those sub-system changes work across your new list of classes.
This is pure speculation and eyeballing but here are my picks for how that process will go for me:
1.)
Archer - Ranger
Armiger - Fighter
Arcanist - Warlock
Berzerker - Defender/Controller*
Executioner - If Rogue is more swash than stab Executioner stays and Thief goes
Harrier - Striker
Hunter - Warlord
Man-at-Arms - Redundant, Could go Leader and renamed Noble
Thief - Striker/Controller*, renamed Rake
Weapon Master - Striker/Defender
*-Cause their secondary abilities let them mess up a whole bunch of combatants at once.
2.) Cleric, Fighter, Paladin, Ranger, Rogue, Warlock, Warlord, and Wizard
3.) Depending on circumstances the Archer, Armiger, Man at Arms, and Paladin might be salvageable. For the right world cleric & wizard should be optional.
4.)
Traits - Can it be balanced against stronger long term races?
Tokens - for the right classes and maybe as a way to do powers
Weapon Profs - 4E seems about right anyways, keep the light vs power distinction?
Defense and Armor=DR - 4E defenses just seem nicer,
Feat Mastery - Meld, some classes yes, others no, or just translate them into power paths
Skill Groups - Meld, get rid of skill points for a class just give each class a set of skill groups for trained, then let them have a number of additional trained slots equal to their INT bonus for individual skills.
Reserve Hitpoints - Probably redundant
Skill Abilities - Some might be redundant with 4E otherwise in like Flynn
General Combat Rules - Case by case, but mostly 4E
Stunts - May need to rebalance for new numbers
Zones - In, unless redundant
Villain Classes - already in 4E, apparently
Wealth Feats - Sure!
I can't think of any others.