Descartes' views as to the relation between mind and body should be understood on the basis of the two main notions he used of "clear and distinct idea" and "doubt", together with the Cogito, "I think, therefore I am".
We can all decide for ourselves if the Cogito is indeed a clear and distinct idea and if I should be in no doubt that I think. If we accept these premises, however, it follows that the thing which is doing the thinking exists. This thing is referred to in the Cogito by the pronoun "I". Descartes explains at length what is this thing, namely the thoughts themselves. So, according to him, there is no doubt that our thoughts exist, at least whenever we are indeed thinking them. The term "mind", in this context, should be understood as referring only to these thoughts, the thoughts that you have at the moment you have them. In this sense, we know our mind exists. Or, rather, our mind knows it exists. Descartes thinks there is no equivalent certainty as to the existence of our body, and indeed gives many examples for why this is so.
Again, we are all free to accept or reject his conclusion in this respect. The main point here, however, is that all that Descartes' Cogito shows is that there is this clear and distinct epistemological difference between the mind and the body: we definitely know our mind exists but we can only believe our body exists. This is if you like an epistemological Dualism and this is all that the Cogito should be understood as supporting.
Descartes went much further than the Cogito but life goes on after the Cogito and we all have to go beyond the Cogito and make up our minds as to the existence of all sorts of things, but this time we have to do that without the support of a clear and distinct argument like the Cogito.
I may be wrong but I don't expect you will find this interpretation in the vast body of literature on the Cogito.
All the same, as I see it, the Cogito works from the first-person perspective and only from the first-person perspective. Crucially, the Cogito is not a claim about other people's mind. Thus, we can only decide for ourselves whether the Cogito is effective as an argument. At least for now, there would be no point in making a claim about the existence or otherwise of somebody else's mind.
All we may need in relation to the Cogito is to understand how it works. There are two basic aspects: whether the Cogito is a valid implication and whether the premise is true. We can easily all agree on the validity of the implication. However, for now at least, each of us is the only person who knows whether he or she is thinking, and therefore whether the premise "I think" is true or not. This is certainly a serious limitation! On the other hand, we can all make up our own mind about that, assuming we have a mind.
If we don't have a mind, I don't think we need to care about the Cogito.
But if you do have a mind, you probably don't need to care much about what people who may not have one say about the Cogito.