As you well know, there are some commentators, who reckon that Enoch was transferred from earth to heaven without seeing death. The new BDAG Lexicon and Louw-Nida both put forth this understanding of Heb. 11:5. William Lane (Word Biblical Commentary) also writes that Enoch did not experience death since he equates the articular infinitival clause TOU MH IDEIN QANATON with the expression in Heb. 2:9, namely, the idiom "taste death." Lane also quotes 1 Clement 9:3: "Let us take Enoch, who having been found righteous in obedience was translated, and death did not happen to him." Cf. Lane, Hebrews, 336-337.
Against this interpretation, however, seems to be John 3:13 and Heb. 6:19-20.
John 3:13 assures us that no man (prior to Christ) ascended to heaven except the Son of Man, who descended from heaven. Heb. 6:19-20 indicates that Christ prepared the way for others to enter the heavens by means of his death and subsequent resurrection. The phrase in Heb. 11:5, while seemingly problematic, may simply be informing us that God made sure Enoch died peacefully without being aware of the pangs of death.
It appears that Enoch did not see death in that God cut his life short and may have placed Enoch in a trance when his life was cut short. Therefore, his death could be identified as a transference.
Gen. 5:24 uses an expression that is commonly implemented as a poetic euphemism for death ("And he was not"); furthermore, the Targum Onkelos says that God caused Enoch to die. The Jewish traditions surrounding
Enoch's death, therefore, makes me wonder whether the Greek METAQESIS was ever used euphemistically.
Compare Genesis Rabba 25.1.
And Enoch walked: He was a righteous man, but he could easily be swayed to return to do evil. Therefore, the Holy One, blessed be He, hastened and took him away and caused him to die before his time. For this reason, Scripture changed [the wording] in [the account of] his demise and wrote, “and he was no longer” in the world to complete his years. — [from Gen. Rabbah 25:1]
ויתהלך חנוך: צדיק היה וקל בדעתו לשוב להרשיע, לפיכך מיהר הקב"ה וסילקו והמיתו קודם זמנו [וזהו ששינה הכתוב במיתתו לכתוב ואיננו בעולם למלאות שנותיו:
for God had taken him: Before his time, like (Ezek. 24:16):“behold I am taking from you the desire of your eyes.” - [from Gen. Rabbah 25:1]
כי לקח אותו: לפני זמנו] כמו (יחזקאל כד טז) הנני לוקח ממך את מחמד עיניך