Here is a family that I believe is from the same area with the Bauldwyn spelling. Not saying this is your man, but it could be a relative. https://www.ancestry.com/genealogy/records/elisha-b-bauldwyn-24-7bvdzr
As you well know when it comes to spelling of names, the Confederates and most other people spelled something the way they heard. My own name evolved from "Pervis"(as spelled in my Grandfathers CSR) to "Purvis" sometime after the formation of Purvis Mississippi. On the other hand, I have heard, there is a Pervis, Texas formed by the same "Purvis" family. The same goes for my "Pitman"- "Pittman" line.
Check this out---https://www.findagrave.com/memorial/10385739/elisha-b.-baldwyn
Using the CWSS I only find one man from Mississippi with the spelling of Bauldwyn, but he was only a Private----
Bauldwin, Charles S.
BATTLE UNIT NAME:
43rd Regiment, Mississippi Infantry
SOLDIER'S RANK IN:
SOLDIER'S RANK OUT:
M232 ROLL 3
General Note - Original filed under Charles S./Baldwin