Let me suggest that there are two different men born about the same year named Andrew Bradshaw. One lived in Tishomingo County MS in 1860; the other lived in Ashley Co. AR in 1860. Mississippi Andrew was born in McNairy Co. TN on Feb. 23, 1818. He married Elizabeth Walker in Tishomingo County MS on Oct. 31, 1845. After she died (ca. 1856) he married Catherine Hafley. The 1860 census lists him with a wife and three children from the two marriages.
Mississippi Andrew died on Feb. 28, 1863.
Arkansas Andrew was born in Mississippi and died about the date you gave in 1863. I really don't know about the exploding Confederates, but wonder if either of these two Andrews enlisted in military service. Do you have evidence along those lines?