I would explain to the group next time you meet that you do not want to be included in the Secret Santa this year, as money is tight. No-one should expect you to contribute to it, and obviously, you are not taking part, so you don't expect a present.
I would not offer any further explanation, and certainly not ask them to donate to charity instead. That to me is being impertinent. They are grown-ups and must decide, as you are doing, for themselves what they want to spend their money on.
You may be surprised by the sigh of relief that goes up from the group when you honestly say you cannot afford this kind of thing in the present circumstances.