Why wouldn't a contribution designated to a missionary be recorded as a Liability instead of an Equity Fund account as you suggest? Then when the money is sent to that missionary the entry would simply reduce the Liability account.
Generally Accepted Accounting Principles (GAAP) states that donor designated gifts, including missions funds, are considered donor restricted funds. As restricted funds it is best practice to record designated gifts as equity accounts, which falls under GAAP standards. This is true regardless of whether the restriction is temporary or permanent. Temporarily restricted gifts are gifts given by the donor for a specific purpose or program or for use at a certain time. In a church, common temporarily restricted funds might include a missions fund, benevolence fund, building fund, and others. Permanently restricted contributions are gifts given by the donor to be permanently maintained, but the church may use any income that comes from the gift. For example, a member gives a substantial amount of cash hoping to maintain a benefit in perpetuity for missions' families. The donor mandates that the funds be invested and only earnings be used by the church to provide college scholarships to missionary children.
While it is not the best practice, if the congregation is comfortable viewing missionary collections and disbursements as debts (liabilities) the missions funds can be recorded as liabilities as long as no external party insists on a financial statement presentation in accordance with GAAP.
For more information on recording designated gifts, see...