FIRST: A last will and testament does not have to be disclosed to anyone  prior to death.
But at death, notice of the commencement of a probate proceeding which is necessary for the will to be given effect must generally be given to:
(1) everyone who takes under the will, and
(2) everyone who would take if either that particular version of the will were invalid and a prior will that it revokes is valid, and
(3) everyone who would take if there were no valid will, and
(4) creditors whose claims are accepted as valid, but are not paid due to the insolvency of the probate estate.
Everyone entitled to notice of the probate of a will is entitled to see the last will and testament submitted to the court in its entirety.
The case could be placed under seal to prevent people other than interested parties and their lawyers from seeing the will, but not sons of a decedent who are interested parties by definition even if they get nothing under the will, because they would take if there was no will.
SECOND: This said, it is easy to make a secret transfer effective upon death via a variety of non-probate transfers such as a beneficiary designation on an account, or the provisions of a trust, that don't require a court proceedings to take effect the way that a will does (people who think that they can avoid probate by having a will are fundamentally mistaken, probate is a court proceeding necessary to give a will legal effect).
Only some of these methods of making a secret gift work if the estate is subject to estate taxes which requires disclosures to be made on gift and estate tax returns of all transfers taking effect at death (something that can be circumvented by making a transfer during life that is not reportable during life because it is within some exception to gift taxation).
 Usually a will has to be shown to the two witnesses to a will, unless it is executed under the recently repealed Louisiana law allowing for a "mystic will" which has seven people witness the envelope but no one witness the will itself prior to death. Of course, holographic wills, substantially in the handwriting of the person writing them, don't have to be witnessed at all.