There are probably some schools that will take just the science LOR's, but very few from what I remember when looking up schools. The only way to find out which ones those are is looking up each individual school and searching for the info on their website or by calling up the schools. It is probably a good idea to develop a professional relationship with a non-science professor now. When I was getting my letters ready, I had the science LOR's all planned out, but no non-science one. I then enrolled in a social science course; after I got an A on the first paper, I went to speak with him, telling him I was planning on applying to medical school and if it were possible to get a LOR. He said it was okay. I gave him my information (resume, personal statement, transcript, etc.), and he actually submitted it before all other LOR's. From what he told me, it was a solid letter. I did manage to get some acceptances.
Good luck.