Each of you can make their own separate will. In their own will he or she makes a specific bequest ( expressed as a set sum of money) or bequests to whatever charity or charities they like. Whoever dies first, it makes no difference to any charity named as receiving a bequest under their will. That charity will get the bequest in their will. On that person's death the survivor can't change the will without the consent of the beneficiaries, in this case the charities. Trusts don't come into it that way
And, in each person's own will they put that the residue of their estate is left to the other spouse, 'if he/she survives me'. (They should say what is to happen to the residue if the other predeceases them).That means that everything remaining, that hasn't been given in the will to the charities, goes to the surviving spouse.
The person can change their own will at any time, by writing a new will which says any previous will is revoked and this will is now the last will, or by writing a codicil to the existing will to alter the sums given as bequests or remove some or all of the bequests. A codicil requires the same legal formalities as a will does.It's usually better to make a new will rather than add a codicil to the existing one. That's the only way of revising the gifts during the lifetime of the person whose will it is, if hardship ensues and the money to charity is needed for themselves or their spouse.
Also a dependent of the deceased can claim for provision to be made for them from the deceased's estate, whatever the will says, in certain circumstances.