I disagree. Look at verse 6 again:
Wherefore I put thee in remembrance that thou stir up the gift of God, which is in thee by the putting on of my hands
Note thou stir up. Paul is not saying the gift was stirred up by the putting on of his hands. Paul is telling Timothy to stir up the gift that is in you by the putting on of my hands
The gift got there by the putting on of hands. Now that may sound like a work to some people, but I don't see how the verse can be interpreted any other way. It is, I believe, a reference to the sacrament of Holy Orders. A sacrament is an outward and visible sign of an inward and spiritual grace. The outward sign is the putting on of hands and the saying of words. The inward grace is the grace to perform the office of (in this case) a bishop.
The office and the grace to perform it are conferred together. Here is what is said in my church when a bishop is consecrated (or made a bishop):
RECEIVE the Holy Ghost for the Office and Work of a Bishop in the Church of God, now committed unto thee by the Imposition of our hands; In the Name of the Father, and of the Son, and of the Holy Ghost. Amen. And remember that thou stir up the grace of God, which is given thee by this Imposition of our hands; for God hath not given us the spirit of fear, but of power, and love, and soberness.
In my mind there is no separation of the office and the spiritual gift.
Its scriptural that Christians can lay their hands on anyone and pray that God would stir up the gift inside them. Its scriptural that any believer can possess one, some, or all of the gifts of the Spirit. Its scriptural that Paul was preparing Timothy for duties in some kind of office. However, the scripture is not at all clear in II Timothy that Paul's laying on of hands is a ceremony making Timothy a bishop. That is something you choose to read into it.