This image I've posted earlier is called "Pipe Major James Wilson" and it seems to be dated 1853, so it's the strongest proof of pipers of 93rd having single-breasted tunics in the time of the Crimean war
This image is of unknown date, but it is about 1854 uniforms and the piper here has similar tunic (and officer and soldier are in pre-1856 coatees)
These paintings by Eugène Louis Lami called "Officers of the 79th Highlanders at Chobham Camp in 1853" and "A Piper of the 79th Highlanders at Chobham Camp in 1853" show us also single-breasted tunic on the piper (but green for 79th Highlanders) along with double-breasted coatees of ofiicers
These pictures are from Osprey's books, they show uniform of 1853 and 1854, but I doubt that they are 100% right, especially if that picture with Wilson is really dated 1853, so I think many details here are taken from 1970s Agryll and Sutherland Highlanders uniforms.