Most trails will still have considerable snow cover above 9500 feet. However, two day hikes are really not sufficient for being acclimated for the altitude of Mt. Whitney. Just go for it, take your time and don't worry. If you start feeling ill, come down to a lower altitude. Enjoy the beauty of the Eastern Sierra Nevada.
One local trail that is snow-free to 8500 feet is the Pine Creek Pass trail, just north of Bishop. Here are the local Forest Service campgrounds:https://www.fs.usda.gov/activity/inyo/recreation/camping-cabins/?recid=20228&actid=29