The purpose of putting the advert in the gazette is to protect you from claims which are made after the deadline in the advert later as you protected yourself by advertising. However, if you do not put an advert in it may be no one will come forward anyway.
In addition as the only beneficiary it is not too complicated if someone comes forward later as it is not as if you will have paid out to numerous beneficiaries and have to try to get money back.
Subject to satisfying yourself of the validity of the debt you would be the one to pay it.
If a debt reduces the value of the estate you can claim a tax adjustment.