I think you need to explain more fully. You say the Pay after Death account (I have never heard of these) was non-probate. Normally, all the deceased's estate is included in the probate - so far as I am aware, the only thing that would not be is something like an insurance policy written in trust with a named beneficiary. Is that what this account is? If so, then the proceeds should go to the named beneficiary. If not, what was the account, how was it used & how was it set up to be outside probate?
You say the wife was the named beneficiary. Do you mean on the PAD account, or in the Will?
The executor has a duty to pay the funeral expenses - they are the first call on the estate assets. However, I am not sure whether this gives the executor the right to take money from a non-probate account to use for this purpose. (If it was an insurance policy written in trust, then I believe the payment would be made direct to the beneficiary, not to the executor, so the issue would not arise.)