I thought it was possible, because the discarding is part of the cost. You also have to pay 2 life with a vampiric tutor or sacrifice an artifact with tinker before you can search your library.
Just wanted to note that while you are correct about Tinker, Vampiric Tutor's life loss is actually an effect of the spell, not part of the cost. So if Tinker is countered the artifact is still sacrificed, whereas if VT is countered you don't lose the life.
Oracle:
Search your library for a card, then shuffle your library and put that card on top of it. You lose 2 life.