Unlike most regiments, historical records of those who served in any of the Guards Regiments are held at the relevant regimental HQ.
Although some records were lost during WWII a letter the Coldstream Guards HQ is the only chance of finding any information on him.
See
http://www.theguardsmuseum.com/Family-Research for contact details.
If you write don't forget to insert "Coldstream Guards Regimental HQ" above the address given.
Good Luck