"Pair Programming's" text says:
"You can play a card with cost 3 or less from another runner's discard (Put that card in their discard afterwards). ..."
I pick "Negotiation" from another runner's discard, which says:
"The next time you buy a Skill card this turn, pay 1 less nuyen for each Skill card you play this turn",
and it's Assist text says:
"The current runner can pay 1 less nuyen for the next card they buy this turn, and then Damage 1 red, 1 colorless)"

I really would prefer the Assist capability of the Negotiation card over its primary one in this case (as it deals two damage), but I am afraid, I cannot do that, as "Pair Programming" allows me to "play" a card (not to "assist") - unless "play a card" includes playing the card as "Assist" (as it's coming from another player's deck ...(?)).

Please advise - Thanks!

You can only play the card 'as if you had it in your hand on your turn'.
Which means you cannot play the card for the ASSIST, only for the base damage and any additional effect in the main section.