No, there's not.
Regularities can be random or they can be caused (if there are causes) but regularities are not proof of causation.
I literally laughed out loud. Causation is unobservable, untestable and superfluous yet you think I'm the one that needs to apply Ockham's Razor?
I think you will see my view is more parsimonious because it stops at the rock bottom way-the-world is without positing the existence of unobservable "causes".
Your view is cumbersome and nonsensical without recognizing that the sort of causation you are talking about doesn't make sense in the context of how logic is applied to observations in a scientific way. We can test for regularities, but regularities in and of themselves are random patterns of occurrence.
The most parsimonious way to go about this is to assume the regularities will continue rather than suggesting other possible regularities, as such regularities do not relate to the world as is has been observed to be. If you introduce the possibility that things could be a different way that has not been observed, you violate parsimony.
The conclusion is to simply adopt the regularity as an axiom until a contradictory observation occurs. By taking the regularites of this sort as axioms to be amended, we develop a logical network to explain certain events. Just as we must take axioms in any application of logic, so too must we take them here. Observation provides the axioms, logic provides their connection. We continually ammend the axioms via observation to make the logical network better fit reality as we observe it.
So we are mindful of the possibility that axioms can shift, since they are not logical in nature, but based in observation, but the logical network that arises from the axioms is a necessary consequence of those axioms. The network shifts with the axioms. We are implicitly mindful of the possibility that the network could shift, but also aware that the conclusions are valid.
Causation is simply manifest AFTER axioms are taken rather than BEFORE. This uncertainty bothers you, but it is the case because we can only work with what we see as we see it. Observational reality is not logical, but logic can be applied to it. Causation is determined afer we pick a logical starting point, the axioms that come out of observation. It is a very simple concept, I would hope that you are not having too much trouble sorting it out.
You can, however, take solace in the fact that you are absolutely right about causation, it is apriori. The problem is that you are assuming it is applied where it is not. If you don't take certain axioms which are implicitly understood to be tentative (based on observation, which could change), then indeed, you do not have causation. Science doesn't deal this way, the (tentative)axioms are taken and logical conclusions are drawn. There is no better way to do this. The sort of causation you are talking about has nothing to do with science, since science is not apriori and thus cannot claim to know the totality of its objects of consideration, so the sort of logical necessity that might be implicit in the objects is not considered(or considerable) by science.
A logically necessary causation that precedes tentative axioms does not exist in science. Once again, to make sure my point is clear, causation is claimed only after certain observation regularities are taken as axioms, so your criticism is akin to pointing at a dog and asking why it argues with your neighbor in Spanish. The accusation does not apply.
Might I suggest that, next time, you make sure you fully grasp the argument at hand before slinging insults. It is more reasonable to assume you misunderstand what was said than to assume the other person does not have any valid point whatsoever. If you don't understand something, please ask and I will clarify.