Yes, you can do that, the same way that grocery stores get you to contribute to food for the hungry charities. The problem is twofold: First, if you will be suspect when you aren't a charity, collecting for charitable purposes; second, you will be likely be audited at some point by the IRS.
Charitable non-profits, as well as other non-profits are regulated for several reasons, the including the government's interest in you actually doing what you say you are going to do with the money and that the proper taxes are paid.
If you really want to do this, do not do it without a lawyer's assistance. It is possible to do, but it is likely that you will get yourself into trouble doing it.
You can certainly do this, but everything that comes in will be considered income to you and then a deduction later when the money goes back out to the charities.
If you are soliciting to the public some states will require a proper registration. That is, a proper non-stock corp would suffice as registration, but being you are not that it could be an issue (although very unlikley on a small scale).
Remember too, that the reason businesses and people give to qualified charitable entities is because those orgs can offer a tax deduction for those donations. This is something you obviously will not be able to do.
You may want to discuss your plans with a lawyer in private and most of us here, including myself, offer a free phone consult. I will also link you to some general helpful info below.
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Most people making charitable donations want a deduction and you would need to have 501 c 3 designation which requires a corporation filing the appropriate forms and receiving permission from the IRS.
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