All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
Your claim that there are no needy people in the present-day is untrue. However, if you are unable to offer the expiation for breaking your oath to needy people (feeding or clothing ten poor people), because you cannot afford it or cannot find eligible recipients of the expiation, you may fast three days as expiation for breaking your oath. The majority of Muslim scholars are of the opinion that the oath-taker is not required to fast the three days successively, although fasting them as such is more prudent so as to stay away from the difference of opinion among scholars. It is incumbent upon the oath-taker to make the intention of fasting these three days as expiation for his broken oath in the night because this is an obligatory fast. As for combining the intentions of fasting the three days of expiation and the voluntary six days of Shawwaal, scholars held different opinions in this regard. The conclusion is that if you intended to fast those days as expiation for breaking your oath, then you have offered the expiation and you will also receive the reward for observing the Sunnah of fasting the six days of Shawwaal (not the reward for fasting them, though), according to some of the scholars.
Allaah Knows best.