The modifier would be applied to the monster stats. In OD&D, humanoid leaders generally have an entire hit die or more than the standard version. So I would apply a modifier to the hit dice rather than just hit points, as well as bonuses to AC and damage.
For example, an Orc +1 would get an extra HD, which includes the corresponding increase in to-hit and saves, as well as +1 to damage and AC.
Orc (HD 1, AC 7, AT: 1 x 1d6)
Orc +1 (HD 2, AC 6, AT: 1 x 1d6+1)
Orc +2 (HD 3, AC 5, AT: 1 x 1d6+2)
For humanoids with less than 1 HD, I would convert the hit dice to nearest die and then add the modifier (for bonuses), or drop the hit dice to the next die (for penalties). For example, a goblin has HD 1-1, which is equivalent to a d6 hit dice. Thus:
Goblin (HD 1-1, AC 6, AT: 1 x 1d6)
Goblin +1 (HD 2d6, AC 5, AT: 1 x 1d6+1)
Goblin -1 (HD 1/2 (1d4), AC 7: AT: 1 x 1d6-1)
As it turns out a system of this nature, but with a different shorthand, was outlined in the D&D Rules Cyclopedia nearly twenty-five years ago. See this post on the The Disoriented Ranger blog for an excerpt of the rules from that volume. It's a little different in that the modifier is applied to hit points per hit dice, similar to a CON bonus. I think this works better for higher HD monsters. With low HD monsters, a one or two point change in hit points won't make a noticeable difference in the staying power of the monster in combat.
One could take this idea further and apply a bell curve roll (e.g. 3d6) to a group of monsters to determine which members are the leaders. Using the B/X stat modifiers, for example:
3: Monster -3
4-5: Monster -2
6-8: Monster -1
13-15: Monster +1
16-17: Monster +2
18: Monster +3
On further thought, rather than rolling for a group, it'd be simpler to just give guidelines:
For every ~20 monsters, one will be +3, two will be +2, and three will be +1.