As already remarked by others: If one tries a narrow interpretation of your question, you are asking a lot. You want someone whose specialty is not mathematics to elucidate a mathematical argument in a way useful and interesting for mathematician in their practice of mathematics, without creating new mathematics.
Interpreted in a slightly broader sense, the first men to come to my mind are Bolzano and Frege.
Bolzano was certainly a philosopher (and priest). His work on what we now consider set theory can very well be regarded as a philosophical elucidation of the mathematical treatment of, I would say, infinite sets, only that prior to Bolzano noone has really thought in these terms! Of course, there is other work by Bolzano, which more purely qualifies as mathematics, as his efforts to put analysis on a firm foundation and his example of a continuous and nowhere differentiable function, which first of all required clear concepts of these terms! But it should be clear that these questions had then a strong philosophical bend; only now that we take these modes of thinking for granted, we can claim that they are just part of mathematics and not philosophy.
Frege is considered by many analytic philosophers as one of the foremost philosophers of the 19th century, although one has to remark that he studied mathematics. In his Begriffsschrift he essentially invented formal predicate logic. In his later work he applied logic to the foundations of mathematics. Formal logic has certainly done a lot for mathematics. Of course, you could claim that formal logic is really the creation of new mathematics, but I think it was not primarly so. Coming up with formal logic was foremost an act of thinking hard about what an argument is - a typical philosophical activity.
There also names like Quine, Kripke and Dana Scott, where part of their works blurs the distinction between set theory, logic, philosophy and mathematics.
Many of the mathematicians active in foundations had also a strong philosophical interest. I want just to mention the names Cantor, Hausdorff, Gödel and MacLane. Their philosophical interests had certainly influence on their mathematics, although this is probably hard to prove.
Even one step further: Mathematicians have certainly done interesting philosophical work on mathematics, even if they do not claim so. I just want to mention Tao's What is good mathematics? and Thurston's On proof and progress in mathematis.
Even more ordinary mathematicians use from time to time phrases like "from a philosophical point of view" in their mathematical musings. One might mark this just as a non-rigorous mode of mathematical thinking, but also as a philosophical-bend mode of thinking - both are correct at the same time, I suppose.