Exegesis:

thrix ek tēs kephalēs humōn ou mē apolētai ‘not a hair of your head will perish,’ proverbial saying promising that they will be invulnerable. This may be understood in a spiritual sense, i.e. that their souls will be absolutely safe, or in the sense that though some will be killed, as a whole or as a community the disciples will be safe (cf. Grundmann). The latter is preferable. ek tēs kephalēs stands for the simple partitive genitive used in 7.38 and 12.7. For ou mē cf. on 1.15.

Translation:

Not a hair of your head will perish (or, ‘be harmed/lost’), or trying better to bring out the emphasis, ‘you will not lose a single one of your hairs-of-the-head’ (Javanese); or again, shifting from negative to positive, and focussing on the person, ‘you will be entirely safe, even to (a single) one of the hairs of your head.’ For hair of one’s head cf. also on 7.38.

Quoted with permission from Reiling, J. and Swellengrebel, J.L. A Handbook on the Gospel of Luke. (UBS Handbook Series). New York: UBS, 1971. For this and other handbooks for translators see here . Make sure to also consult the Handbook on the Gospel of Mark for parallel or similar verses.