In 1 Peter 2:17, the operative word is βασιλεύς (basileus) which is definitely "king" in English, and occurs about 115 times in the NT, eg, Matt 1:6, 2:1, 5:35, 10:18, etc. Thayer offers the following meaning: "leader of the people, prince, commander, lord of the land, king". When this refers unambiguously to the Caesar, it could be translated, Emperor".
In 1 Peter 2:17, only "king" is defensible unambiguously as it simply refers to the local head of government, whoever that might be, without excluding Caesar.
The word "Emperor" is Σεβαστός (Sebastos) and occurs only three times in the NT, namely, Acts 25:21, 25, 27:1. Its meaning is clear: it was the official Latin title of the "Augustus", the emperor of Rome. Note the meaning from Thayer:
ὁ σεβαστός, Latin augustus, the title of the Roman emperors: Acts 25:21, 25 (Strabo, Lucian, Herodian, Dio Cassius, others); adjective
σεβαστός, σεβαστη, Σεβαστόν, Augustan, i. e. taking its name from the
emperor; a title of honor which used to be given to certain legions,
or cohorts, or battalions, for valor (ala augusta ob virtutem
appellata. Corpus inscriptions Latin vii. n. 340, 341, 344): σπείρης
Σεβαστῆς, the Augustan (Imperial) cohort, Acts 27:1 (λεγεών σεβαστη,
Ptolemy, 2, 3, 30; 2, 9, 18; 4, 3, 30). The subject is fully treated
by Schürer in the Zeitsehr. für wissensch. Theol. for 1875, p. 413ff