Since +Marshall Brengle just asked a question about race-as-modifier vs. race-as-class over at the Black Hack discussion community on Google+, I thought I'd toss out the ideas I've been bouncing around on the matter.
Since virtually everything works on stat checks in The Black Hack, the simplest way to bring in races is just with stat modifiers. Roll for stats as per the rules, then apply the following modifiers.
Dwarves: +1 to CON, -1 to CHR
Elves: +1 to INT, -1 to CON
Halflings: +1 to DEX, -1 to STR
If I went this route I might bump the modifiers up to +/-2 instead, to make the modifiers themselves more meaningful. While this is slim on flavor, it does keep everything streamlined. This is the way I'd do things if I were to run a game for players who wanted races but disliked (or didn't care) about race-as-class. Modify your stats and then pick a class as normal.
That said, it would not be terribly difficult to actually come up with a new class for TBH. Lots of people are already doing so, both at the discussion community as well as over at RPGNow (e.g. +Mark Craddock's The Class Hack). While I don't think Brie and I are going to convert our current game to TBH (at least not in the immediate future), I have thought about it and I'd probably do something like this if we did:
Starting HP: d6+4
HP Per Level/Resting: 1d6
Weapons and Armor: All except Plate & Mail.
Attack Damage: 1d6/1d4 Unarmed or Improvising.
Roll with Advantage when using WIS to search for secret doors.
Roll with Advantage when saving vs. effects caused by undead.
Roll to see if attributes increase, roll twice for INT and DEX.
Elves can cast a number of Arcane Spells per day according to the Daily Elf Spells table below.
Elves start with a large spellbook containing a total of 1d4+1 spells from the Level 1 and 2 Arcane Spell Lists.