vietvet191, Your LRH C96, with serial number in the 31,000 range falls in the range of C96s that had a good deal of variation, if its a Mauser made C96. 9 x 19 mm chambering is not one of them. Your description of "serious rust under the grips" does indicate it is one of the thousands that were imported from China. Though the majority of these were M1930 models there were also many early and rare model variations that came in during the importation. Many of these examples had seriously rusted grip loops and very poor bores and were re-lined to 9mm. There is also the possibility that it is a Chinese made copy of the C96. A picture will tell the tale if you can post some it will help us tell you what you have.
Regards,