My first suggestion was to look at John Barrien Lindsley's Military Annals of Tennessee. I skimmed thru the online version at Cornell and don't think it will be of any help. Memorial list for 31st Inf starts page 468 and 16 Cav starts page 735.
Calvin Morgan Smith's diary is available from the Hawkins County Genealogical Society in Rogersville TN. It is listed as $5 + $3.95 s/h + .49 tax. Go to their website for how to order.