The Ba’al Halachot Gedolot (a halachic code of the Geonic period), which the Beit Yosef also quotes, understands “mi’shetishka hachama” as being very definite – namely, not before sunset. And so does the Rambam (as can be seen from the way he quotes and explains the text). Thus, the baraisa’s language sets the time frame of lighting and one may not light either before or after.
The Darchei Moshe – the commentary on the Tur by the Rema – notes that one who has missed lighting menorah on one of the nights of Chanukah should proceed to light the normal number of candles on subsequent nights. He cites the Maharil (Morenu HaRav Yaakov HaLevi Moellin, 14th-15th century, Mainz) and the Aguddah as his sources; he disputes the Maharam of Rothenburg who suggests that if one has not lit on the first night of Chanukah, one should only light one candle on the second night because it is the first night of lighting for him.
In the Shulchan Aruch (Orach Chayim 672), the Mechaber states (as he did in his explanation on the Rashba’s responsum) that one cannot compensate for missing lighting menorah – “ein lo tashlumin.” The Rema (ad loc.) remarks: “But he lights on subsequent nights,” adding (as in his Darchei Moshe commentary on the Tur) that he should not act differently than other people (i.e., he should light the same number of candles they light). The fact that the Rema finds it necessary to make this remark suggests that the Mechaber does not agree that he may light menorah on subsequent nights – which is at odds with his commentary (Beit Yosef) on the Tur.
According to the Ateret Zekeinim (ad loc.) we might explain the Rema’s understanding of the Mechaber’s “ein lo tashlumin,” not as prohibiting lighting on subsequent nights, but as referring to compensation for having lit fewer than the required numbers of candles on a particular night. He may add such candle(s) the next night without reciting additional blessings (as per the Orchot Chayim, quoted earlier).
The Gra explains that the mitzvah of lighting menorah is similar to the mitzvah of dwelling in a sukkah. We may erect a sukkah on Chol Hamo’ed if it was not possible to do so before the festival because the mitzvah of eating and sitting in a sukkah applies each and every day of the holiday. Likewise, the miracle of the oil took place on each of the eight days of Chanukah. Therefore, lighting menorah is obligatory on every night of Chanukah. He adds that it is not similar to counting omer, where omitting a single day causes a breach in the continuity of the count, since the Torah specifically states about the omer (Vayikra 23:15): “Sheva Shabbatot temimot tihyena – Seven complete weeks shall there be.”
It is abundantly clear from all of the above that a person who misses lighting menorah on one night should light menorah on subsequent nights.
As for your situation, you will either be at the airport or on an airplane at the time when lighting menorah becomes obligatory – both being places where authorities do not permit lighting a flame. As such, you are considered an onnes, a person who is prevented from fulfilling a mitzvah due to circumstances beyond his control. Hence, the rule “onnes rachmana patrei – one who is prevented due to circumstances beyond one’s control is relieved of one’s obligation” applies.
After submitting your original question, you showed me small battery-powered bulbs which you would be allowed to light on an airplane. That brings us to the following discussion.
Rabbi Chayim Ozer Grodzinski (Responsa Achiezer, Orach Chayim 6) discusses electricity on Shabbat. Quoting R. Yitzhak Shmelkes (Minhat Yitzhak, Yoreh De’ah, Responsum 120; Yoreh De’ah Vol. 2, Responsum 31), he refers to the liabilities incurred for kibbui (extinguishing), which is not allowed on Shabbat, and equates electricity with a flame. He permits reciting the proper blessing (over electric lights) for the mitzvah of lighting Shabbat candles, but adds that regarding Chanukah, one should use olive oil to fulfill the mitzvah in its optimal fashion.
Rabbi Grodzinski thus leaves us with the possibility of kindling nerot Chanukah with electric lights. However, we assume from his discussion that this would be without reciting the blessings.