No, not quite. The direct translation is more "I should refrain from drinking that", which would normally be expressed in English as "I should not drink that".
I see where I went wrong now - there would need to be a "ddim" after "Ddylwn i" to make it "I should not." Thank you!
- ddylwn i ddim yfed
- dylwn i beidio ag yfed
- fe/mi ddylwn i beidio ag yfed
All mean 'I should not drink' There is no reason for the mutation of ddylwn... in the original sentence, as there is no fe/mi marker or anything else to cause it.