The core ruling is unambiguous: Shulchan Arukh, Orach Chayim 531:2 states that one may not shave or cut hair during Chol HaMoed, even if he was prevented from doing so before the festival, and Arukh HaShulchan, Orach Chaim 531:1 explains that this prohibition exists precisely so that people will not postpone their preparations and come into the festival unkempt.
The reasoning behind this, as given in Moed Katan 14a:3 and Mishnah Berurah 531:3, is that if shaving were permitted during the festival days themselves, everyone would rely on that leniency and enter the festival disheveled, so the practice is barred even for someone genuinely unable to shave beforehand.
The Mishnah and Gemara in Mishnah Moed Katan 3:1, Moed Katan 13b:15, and Moed Katan 17b:3 list a narrow set of exceptions — one returning from overseas, from captivity, from prison, one released from a ban of nazirite status, or a leper completing purification — but only where there was no opportunity (פנאי) to shave before the festival began; one who had such an opportunity remains forbidden even if he falls into one of these categories.
Contemporary codification confirms this remains the operative halacha: Kitzur Shulchan Arukh Yalkut Yosef, Orach Chaim 531:1 states that one does not shave or cut hair on Chol HaMoed even under constraint, and Kitzur Shulchan Arukh Yalkut Yosef, Orach Chaim 531:3 adds that even someone who shaved with a machine or depilatory before the festival may not shave again during Chol HaMoed, noting that most later authorities rejected a lenient view permitting it for a poor laborer.
Modern responsa applying this to practical situations reinforce the stringency: Rav Mordechai Eliyahu (Shut HaRav HaRashi 36:26) rules that one must shave before the festival if that is his practice, and that shaving during Chol HaMoed is forbidden even if one already shaved before Yom Tov, stressing this is especially strict for public figures whom the community watches and learns from; and Rav Mordechai Eliyahu (Shut HaRav HaRashi 36:25) rules flatly that there is no permission whatsoever to shave during Chol HaMoed, following the Shulchan Arukh's prohibition.
None of these sources carve out an exception for a job interview or similar personal need, and the exceptions that do exist in Mishnah Moed Katan 3:1 and Moed Katan 17b:3 are limited to cases where there was literally no time to shave before the festival began, not cases of convenience arising during the festival itself.