All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Shaking hands with a Kafir (Jew, Christian or others) is not among the nullifiers of ablution. In fact, the impurity of the Kafir is not physical, it is immaterial. This is the impurity stated in the verse. Allah Says (what means): {O you who have believed, indeed the polytheists are unclean, so let them not approach al-Masjid al-Haram after this, their [final] year.} [Quran 9: 28]
For more benefit on greeting non-Muslims, please refer to Fatwa 88513, 83602 and 84225.
Allah knows best.