I think the most natural English rendering of 'ขาดคุณนางฟ้าไปผมคงมีชีวิตต่อไปไม่ได้แล้ว' is: 'Without you, my angel, I probably couldn't go on living.'
That version keeps the original's intensity and the affectionate address 'my angel.' Using 'probably' mirrors the Thai 'คง' which softens absolute statements a bit — it reads like someone caught between despair and sincere emotion. The phrase 'couldn't go on living' is slightly dramatic and fits well in a heartfelt confession, a letter, or a climactic scene in a romance drama. It preserves the speaker's vulnerability while sounding natural in English.
If a different shade is wanted, small tweaks change the tone: 'I couldn't bear to live without you, my angel' is more poetic and immediate; 'I'd be lost without you' feels more conversational and less fatal. Because 'ผม' signals a male speaker in Thai, keeping 'I' straightforward in English is fine; gendered nuance rarely needs explicit marking unless you want to use 'my dear' or a specific name. Personally, when I imagine delivering this line aloud, the original translation—'Without you, my angel, I probably couldn't go on living'—captures that tense mix of love and helplessness perfectly, making it powerful without feeling stilted.