Can a 1st level spell from the aberrant dragonmark be casted by soley pact magic spell slots from a warlock?

For an adventure in D&D 5e starting at level 1 I have created a variant human warlock, with the feat aberrant dragonmark. I have chosen witch bolt as my first level spell from the feat.

In addition, choose a 1st-level spell from the sorcerer spell list. You learn that spell and can cast it through your mark.

My problem is from the that fact that the spell comes from the sorcerer spell list and makes me question, could I even be able to cast witch bolt using pact magic spell slots because it can also be found on the warlock spell list? If I can cast it, then my next question would be would be under the mark’s spell modifier (constitution) or or my warlock spell modifier (charisma)?