"I do not sing but I play the violin."
Translation:Nem énekelek, hanem hegedülök.
No. If pedig is in the first position of the second clause, it means although /even though, so "Nem énekelek, pedig hegedülök" would mean "I do not sing, even though I play the violin", which is pretty different.
If it's in the second position, pedig has a similar (but not exactly the same) meaning as hanem, but the two conjunctions require a different structure and wording.
- "Nem ezt kérem, hanem azt." -- "I don't want this, but that." (nem ezt -- hanem azt)
- "Ezt nem kérem, azt pedig igen." -- "I don't want this, and I want that." (ezt nem -- azt pedig igen)
As you can see, hanem comes before the word it refers to, while pedig comes after it (if used in its "contrasting and" meaning), and that is reflected in the first clause as well in the position of nem.