There are two different notions at work in this discussion that need to be explored: dispensation and exception. They are not the same, even though they would have the same net effect.
True, a dispensation can relax the law so that a non Catholic wedding ceremony can result in a valid marriage involving a Catholic. However, the presence of a Catholic cleric at a non Catholic wedding ceremony is not required as a prerequisite for the granting of the dispensation mentioned in canon 1127 or for validity once dispensation is given. (I would have no idea of a basis in canon law by which the necessary presence of a Catholic cleric at a non Catholic ceremony could be asserted.)
But it is also true that the law itself can except a Catholic from the requirement of canonical form. In such a case, there is no need of dispensation.
Now, the matrimonial law of the Church places 3 exceptions in the case of Catholics who have defected from the Church by a formal act. They relate to 1) the obligation of the canonical form of marriage for validity, 2) the invalidating impediment of disparity of cult, and 3) the prohibition against marrying a non Catholic without permission.
At the beginning though, it is necessary to recall that certain conditions and actions must be present for such a formal defection to occur. These should be viewed at
clsa.org/content/node/184 before proceeding. That document will treat the details.
These canons and notions will be involved.
Unless there is a dispensation or exception in the law, Catholics must celebrate marriage according to the Catholic form of marriage, or the marriage is invalid (canons 1117 and 1108§1). The exception would be operative for the formally defected Catholic.
Unless there is a dispensation or exception in the law, Catholics cannot marry an unbaptized person, or the marriage is invalid (canon 1086 §1). The exception would be operative for the formally defected Catholic.
Unless there is a permission or exception in the law, a Catholic cannot marry a non Catholic, or the marriage is illicit, that is, contrary to canon law (canon 1124). Validity is not affected. The exception would be operative for the formally defected Catholic.