JD, thanks for your feedback. I looked over the OPC BCO. As I read it, and I'm willing to be corrected, there seems to be a broader use of the word "Church." It appears capitalized, which typically indicates a broader use (denominational).
For everyone's reference:
4. The Bringing of Offerings
a. The bringing of offerings in the public assembly of God's people on the Lord's Day is a solemn act of worship to almighty God. The people of God are to set aside to him the firstfruits of their labors; in so doing, they should present themselves with thanksgiving as a living sacrifice to God. All should participate in this act of worship when God gives opportunity for it. Parents are to instruct and encourage their children by precept and example to give of their substance regularly, purposefully, generously, and joyfully to the Lord through his church.
b. It is the duty of the pastor, since he is to proclaim to the people the whole counsel of God, to cultivate biblical stewardship and the grace of liberal giving in the members of the church. He should remind them of the admonition in Scripture that everyone is to give as the Lord has prospered him, of the assurance of Scripture that God loves a cheerful giver, and of the blessed example of the Lord Jesus Christ, who, though he was rich, became poor, in order that poor sinners through his poverty might become rich.
c. The session shall take care that the offerings of the congregation are used only for biblical purposes, such as the maintenance of public worship, the preaching of the gospel throughout the world, the ministry of mercy in Christ's name, and other Christian objects. The offering ordinarily should not be used to transmit funds to causes other than the ministries of the Church. If a member of the Church designates a gift to a particular cause, it shall be the responsibility of the session to determine, before the gift is accepted, if it is appropriate to support that cause through the Church or if the gift should be returned to the donor.
d. It is desirable that Christian love be demonstrated by offerings for the use of the deacons in the ministry of mercy on behalf of the church. It is appropriate that a special offering be received for this purpose following the Lord's Supper.
You might be correct about the broader use of "Church" in the section, but nonetheless it seems to me that all offerings are funnelled (as it were) through the session, whose job it is to steward the funds faithfully. A pastor is a participant in corporate worship if not a member of the particular church, and as God gives him oppurtunity to give he should do so at the appointed time in the service. If he wants his offering to go elsewhere other than the ministries of his particular church, it seems like that would be a choice requiring approval from the session.