Even a monk will incur TWF penalties for making an unarmed strike. From a rules standpoint, fighting with kukri/fist or kukri/headbutt is the same as fighting with kukri/kama, which is the same as fighting with longsword/dagger, or any other two-weapon style.
Well.... unless he's using a special monk weapon.
"A monk fighting with a one-handed weapon can make an unarmed strike as an off-hand attack, but she suffers the standard penalties for two-weapon fighting. Likewise, a monk with a weapon (other than a special monk weapon) in her off hand gets an extra attack with that weapon but suffers the usual penalties for two-weapon fighting and can't strike with a flurry of blows."