CollectionAssert.AreEquivalent is implemented as:
Assert.That(actual, new CollectionEquivalentConstraint(expected), message, args);
You can write out your assert that way and supply a custom IEqualityComparer with Using:
Assert.That(actual,
new CollectionEquivalentConstraint(expected).Using(customComparer));
You can also shorten new CollectionEquivalentConstraint to Is.EquivalentTo:
Assert.That(actual, Is.EquivalentTo(expected).Using(customComparer));