The only Stewart I can find in the 1st Regt of Foot in the Crimean Medal rolls, after about 15 minutes of scrolling through their medal rolls was 2876 Private James Stewart, entitled to a Crimean Medal p 104 and Sebastopol Clasp p 71.
It is possible that he served in the regiment and never went to the Crimea. If so, his name should appear on the Depot Rolls of the regiment, which can be seen at the National Archives at Kew.
I may have missed his name, but I don't think so, although the legibility of the scans is sometimes very bad. If you want to check these first, you can find a CD of the medal rolls available online. I can recommend an inexpensive researcher at the NA if you want to go that route.